I'm new to posting here but have been reading up on as much as I can about these bikes for a few months. I have an '05 Boulevard S40 that had been parked for 5 years or so until I got my hands on it.

I was able to get it running with a good carb clean and new jets, new air filter, oil change, new plug, and fresh gas. As well as some of the basic recommended mods from around here like a Raptor petcock.

I've been through the carb fully twice.
Once with some brushes and carb spray, and a random Amazon jet kit. This got it good enough to run but would bog out with more than 1/2-3/4 throttle, and it liked having the choke on all the time. But it was good enough to ride it to my shop space across town where I could dig into it further.
So I went through it a second time, this time running the body through a buddy's ultrasonic cleaner. After that it was struggling to idle. I found that I had the larger pilot air jet and the main jet switched, and also opted to get an AllBallsRacing jet kit to replace the no-name Amazon kit.

This is where my problems have really begun. Currently the bike will fire up from cold pretty easily, the idle is a little lope-y, but it seems fast enough to avoid the oil starvation issues of a slow idle. As it heats up, it begins to cough a little black smoke, and once it gets fully hot it will simply die from being too rich. It will stay running if you are on the throttle, but it spews black smoke, especially if you give it a good hard blip. The plug is always fouled with gas, black and damp. It is basically unrideable as anytime you have to stop and let it idle it tries to die out. This is all with the pilot screw all the way in. It only gets worse as I turn it out.

I have verified all the jets are the correct sizes, in the correct places, save for the smaller-bodied pilot air jet under the needle diaphragm is a bit big. (I tossed the original jets the first time I replaced them. I know, I'm an idiot). I've checked the float/fuel level in the bowl and it appears to be within spec. I've done a valve adjustment. The spacer on the needle is stock, not cut down like is suggested for a lean throttle. It does have an exhaust leak in the muffler. The air box is clean, no blockage. I am going to try running it without the air filter to see if that improves things when I have time.

It feels like I should be back at a basically stock carb now, so this constant super rich running issue is really confusing me. I feel like I've hit a wall on this project. I'm probably going to pick up a brand-used carb from a junkyard in the area if they've got one, if nothing else for spare parts.

This is all the relevant info I can think of right now, if you need more, please let me know. I'd really appreciate any suggestions you have for me, as I really am not sure where to go from here.
Thanks in advance!

It's not mysterious at all.  You know what one of the problems is...the junk set of jets. You said one of them is a tad large, but if the jet came out of one of those kits you don't know what size it is.

You need a known good set of OEM spec jets. You could measure the jets you have, but the pin gauges needed to measure them would cost as much as OEM jets.    

And be sure to check the upper air jets if you changed them.  People have mixed those up with the lower jets before.  

Are you missing washers under any of the jets?  I don't know if your carb even had any.  If you don't know, you'll need to do some research.  And triple-check that float level.  And don't forget to make sure the vacuum line is plugged like Paul said.

And did you change the oil before you replaced the petcock?  If you did you might want to be sure there is no gas in it.

I would not suspect the rings at this point.......it appears you have a carb issue and are just dumping too much fuel into the fuel/air mix.

The holes in the bottom of the slide are what allow the vacuum in the venturi to get on top of the slide/diaphragm and raise the slide.  When the vacuum is low the slide drops....when the vacuum is high the slide rises.

If the float level is correct and the float bowl is not overflowing - then the chances of filling your crankcase and airbox with fuel is not going to be an issue.  The other way the crankcase/airbox get filled with fuel is when the diaphragm in the stock vacuum operated petcock fails and allows fuel to flow down the vacuum line.  If you have a smell in your oil currently, it is likely from the overly rich fuel/air mix.

I suspect that you just don't have the jets in the proper place.  I would start with a #150 main jet and a #50 or #52.5 pilot jet.  Make sure the other jets are in their proper place.

What is the condition of the diaphragm in the TEV (Throttle Enrichment Valve).  Those get stiff and won't work as they age.

I likely have a good stock carb....I will look and see what I have.

Those 2 holes in the slide need to be there....without them the slide will not ever rise, and you will never get above an idle speed.

The size of the holes is also somewhat critical, as they determine how quickly the slide will respond to changes in the engine vacuum when you twist the throttle and open the butterfly.  Smaller holes will give more time for slide to rise - larger holes will make it happen faster.

Changing the size of the holes is risky - if the holes are too large the slide could rise too quickly and you will lose the "Constant Velocity" benefits.  The slide could lift quickly and allow the vacuum to drop - which would then allow the slide to drop.....it could get into some weird oscillation.

When I clean carbs, I never remove any of the jets in the carb inlet or the top where the diaphragm is located.  I only remove the pilot and main jet - the air correction jets never seem to get corroded or plugged up.  I never have to worry about getting them in the right place if I never take them out!

Dave, thanks for the info on the slide.

Mike, I think you're probably right about the jet kits. I'd like to basically start from scratch with good jets, and if you say Jets-R-Us is reliable I'll go through them.
It looks like they don't list anything for our specific carb model, BS40 if I'm not mistake. So do you know if the jets in our carbs cross with to another more common model? Otherwise I'll pull them all out and take measurements of them to compare to the listed dimensions on the website.
If you've got any suggestions for identifying the jets, or even just specifically which ones I need, I'd appreciate it.

Lucme, the Mikuni jets for the stock carburetor are designated in millimeters.  So, if the specified jet is a #145 the orifice is 1.45mm.  The stock jetting for your 2005 carburetor is as follows:

Main Jet:         #145 = 1.45mm = .057"

Pilot Jet:          #52.5 = 0.525mm = .0207"

Pilot Air Jet 1:   #45 = 0.45mm = .0177"

Pilot Air Jet 2:   #230 = 2.30mm = .0906"

The jets are expensive, and from what I understand you haven't modified your engine much, so I would stick with the stock jet sizes until you get the thing running correctly.  You need to establish a baseline first.  The only way to do that is get it back to the stock setup.  If you have a free flowing airfilter and a less restrictive muffler, then maybe install a 147.5 or a 150 main jet, all the other jets should be stock size.  It will run lean and hicup and take forever to warm up, but it will run.  From that point you can make changes (never more than one thing at a time) and dial it in.  These carbs really only need the slide needle raised up a bit and the mixture screw backed out a bit.

Measuring the jets is tough unless you have pin gages.  You can do some crude checks with numbered drills, but don't expect any real degree of accuracy.

For the pilot jet, a #76 drill should just go in, and a #75 should not.

For the main jet, a #54 drill should just go in, and a #53 should not.

For PAJ #1, a #78 drill should just go in, and a #77 should not.

For PAJ #2, a #43 drill should just go in, and a #42 should not.

If you use numbered drills to check sizes, you do not want to insert the cutting edge of the drill bit, you insert the shank so as not to damage the jet.  Use a light touch, never force the steel bit into the jet.  If you have a miniature numbered drill set, it would be most beneficial to know what's in the carb now.  It might help you to understand the problem better and also you could share that with us so we can learn too.  You can purchase a miniature numbered drill set from any decent hobby shop.  For PAJ #2 you can do a crude check with fractional drills (5/64" & 3/32"); close enough for diagnostics.

Getting a set of correctly sized jets is the easy part of your problem.  IMO, the lion's share of your issue stems from the slide needle, needle jet, and idle mixture screw.  Those items are harder to come by.  So, in an effort to get you on the road again, I humbly ask for your assistance.

Again:

What color is your needle jet?  Is it silver indicating stainless steel, or is it yellow indicating brass?

What color is your slide needle?  Is it silver indicating anodized aluminum, or is it yellow indicating brass?

Is your mixture screw long like the bogus screw identified in my old post, or is it short like the old post shows?

Can you post some pictures so we can actually see what you are working with?

I told you it wasn't mysterious!!  (It will be mysterious if the correct jets don't solve your problem but you have to start with a "known good" parts.)

Jets R Us shafted me once.  They made a mistake on my order and refused to send me the correct jet until I shipped the wrong jet back.  The shipping was more than the cost of the jet.  Pretty crappy since their policy is NO RETURNS because they claim they can't resell the jet since it could have been modified.

They are a good source if they send you what you ordered.  You can also go through Partzilla or some other reputable mail-order parts company.