I finally got some parts and have an update.  I was able to replace the idle/mix screw with a stock part.  I also replaced the o-ring, washer and spring.  Basically, the entire idle/mix screw assembly has been replaced with known good stock parts.

While the carb was out, I gave it another thorough cleaning, ensuring cleaner went through all the ports, holes, etc.  I think the carb is in good shape.

I put it all back together, fired it up, and no change.  Dang it!  The idle is still rough, idle/mix screw has no effect, knurled knob has to be all the way in to even idle.

So, I took a break to think about it.  I remember one of the things the previous owner said, "my mechanic said it needs a valve adjustment".  That didn't sound right since this engine only has 3k miles.  But, I do remember an old Craftsman riding mower that ran terrible and the YouTubers said to adjust the valves.  I remember doing that on the lawn mower and it ran way better.  So, why not give it a go I figured.  It'll be a good learning experience.

Here's what happened, and I would like to know if this is normal.  When I removed the valve timing inspection cover (the one with the big slot that you have to get creative to remove), gasoline came POURING out.  Holy smokes!  I wasn't ready for that and quickly screwed it back in.  Then, I got my oil change containers in place and removed the cover again.  There's had to be 2 quarts of gasoline that came out.  It's actually mixed with some oil it seems, but the consistency is a lot more gas than oil.

Nothing in the manual or the valve adjustment procedure on here said anything to the effect of "and get something in place to catch all the gas that comes pouring out".  So, that leads me to believe this may be a clue as to what is going on.

Is it normal to have a bunch of gas spill out when you remove the timing inspection cover?

Results of the valve adjustment:  they were not gapped appropriately and had zero clearance when the engine was at TDC.  So, I loosened them up to spec.  Also, the book calls for adjusting the automatic decompression cable prior to the value adjustment.  So, I checked that first.
That didn't have the recommended amount of slack when the engine was at TDC either.  So, I adjusted that to spec as well.

I'm getting ready to go double check all my adjustments and wanted to get some feedback on the gas spilling out before bolting everything back up.  I could see maybe some oil in there, but not gas.  That doesn't sound right.

Thoughts?

Thanks for the info Justin.  So this is a recent development.  I've been changing the oil very frequently on this bike trying to clean out the engine.  Since my last oil change (which didn't have gas in it), I probably rode it 1 or 2 times.  The float valve in the carb was also dorked up, so I'm guessing it allowed the lower end to get flooded.

I just pulled off the oil plug on the bottom and sure enough, fuel.  

I'm cleaning it all out with compressed air and so forth like you suggested and then I'll add some fresh oil (I'm changing the filter too most definitely).  I'm pretty sure I corrected the float issue as well, but I'm going to do the float level check to be sure.  I bet that's what let the fuel into the bottom.

Thanks for the help!

When the petcock leaks, or if it is left in the “on” position, the float needle valve in the carb eventually starts to leak.  Then the carb overflows.  But these emission-compliant carbs don’t have an overflow tube.  So, the gas dribbles out into the venturi of the carb.  From the venturi, the fuel runs into the intake manifold.
 
The fuel can also run the other direction, into the airbox.  Happens all the time.  The airbox fills up with gas.  You already know gas is getting into your oil.  That’s from fuel running down your intake manifold.  You need to know if gas is also getting into your airbox. Open your airbox and remove your air filter.

Is there gas in your air box?

Is the air filter element soaked with gas?


If the air box and filter are filled with gas, you must dry them out.
 
You can drain the airbox and then mop it up with paper towels.  Be careful.  Dispose of the flammable liquids and materials in a safe manner.

You can let the filter element air-dry.  Do that outdoors, not in the garage or house.

DragBikeMike:  I just read your write up on the carb rebuild kit from eBay.  Holy smokes!  I think that's exactly what happened with this bike!  All the clues point to that.  It's amazing how those small differences in parts can dork up a bike so much.  Wow!

So far I've had to replace an unmarked pilot jet, unmarked main jet, and the infamous idle/mix screw that looked exactly like what you got on ebay.  

I'm going to do a full tear down on this carb and post pics.  You're right--everything in that carb that I haven't yet replaced is suspect now.

Ok here's the answers to the questions you posted:

Is your petcock a genuine Yamaha part? Yes.  Just double checked part number from the website I ordered from.  It's the real deal.  I seem to remember it coming in Yamaha packaging too.

Do you ALWAYS turn off your petcock when you shut down your bike?  No.  And this petcock was definitely left in the on position.  That's a bad habit that changes today.  So I'm guessing it filled the bowl up and dribbled past the float valve to both to the intake manifold as well as the air box?  

Is your petcock leaking?  I really don't believe so.  I've had the tank pulled off the bike several times, shut the petcock off, and no leaking.  Also, I've had the tank on, fuel line from the petcock dangling, and the petcock off with no leaking.

Is there gas in your air box? I haven't looked since the gas-in-the-engine incident, but I'll guess a "yes".  When I pull the carb I'll confirm and let you know.

Is the air filter element soaked with gas?  I'm guessing yes, but again I'll confirm when I pull the carb to do the tear down.

Is your needle jet silver or is it brass?
Is your slide needle anodized aluminum or is it brass? Pics will be posted soon of all the carb internal parts.  My guess is that these parts are "junk brass".  That's what I seem to remember, but let's find out.

Are your jets unmarked?     The pilot and main sure were unmarked initially, but I've since replaced them with Mikuni jets.

Mike thanks for that write up on the ebay rebuild kit.  Man that gives me some relief that the focus of this bike is back on the carb.  When I replaced that idle mix screw, and so no change, I was totally disheartened.  "Well, if the carb is 100% good, and it's still running like crap, then something is majorly screwed up in the engine" I thought.  That led me to the value check (which was probably needed anyhow, and a good learning experience, and most importantly led me to find all the gas in the crankcase).  I'm so happy that the issues may yet still be junk carb parts and not a cracked piston cylinder cam o-ring valve seat fantabulator deep inside the engine  .

Ok I'll give the air box a once over and also post a batch of pictures of my carb's guts with annotations, hopefully today if I can swing it.  I'm like a NASCAR pit crew member pulling that carb off now.

Thanks again for all the help.

Will, did you say that all of the fuel/oil came out of the valve cover when you went to adjust the valves? There is a mesh breather in the head that can be soaked with fuel. This will have to be replaced.

@Dave can give you the details if this problem exists.

Got it. I reread it.

It was definitely your wife's cats.  I am certain of it.