Hello everyone,
My first post. I purchased a non-running 2007 S40 about two months ago and I need some ideas from those who are more experienced. The bike sat about 2 years. It came with a Harley Dyna muffler. Luckily the prior owner drained the carburetor prior to letting it sit. I cleaned out the fuel, change the petcock to Raptor style, added a fuel filter, new battery, got it running, ran it with Seafoam added, cleaned out the fuel again with fresh fuel, and got new tires. It was backfiring like CRAZY at every lift off of the throttle. The carburetor had 52.5 and 140 jets. I removed the carb, sprayed it out since it looked very clean, and changed out to new 52.5 and 152.5 jets.

This is where it gets confusing.  Based on what I found online, I, took out the white spacer on the needle and replaced it with two washer shims at the same location. I also turned out the mixture screw to three full turns. It had a huge leak at the juncture of the Dyna muffler so I got a new Dyna muffler and an adapter and got things sealed up.

All of this helped about 30% in reduction of backfire. The exhaust is the only real modification although KN filter may be in the future. But the backfire at throttle liftoff is still happening. Just for kicks, I rode it with half choke on (which I didn't even know it had until recently) and it burbles but didn't backfire on liftoff. Stuff I have seen online are all over the place as to jetting but indicates that I should be close to the proper setup for what I have.

The biggest confusion for me is the shims.  Some places say sand it down half way, which is basically the same as replacing it with two metal washers (which is what I have done).  Other places say leave the white washer alone because of required spring tension and put one metal washer on the main of the needle below the white washer.  Which is it? I am so confused about where the metal washers actually go and what to do with the white washer!
What do I try next?  If the 2 metal washers replace the white one at the same location, I am inclined to take one of the metal washers out, which should cause the needle to rise higher and let in more fuel right?  And that should help with backfire.  Am I on the right track here?

I would appreciate your thoughtful insight. Thanks in advance.

Thank you for your help.  I didn't look at the tev because the main diaphragm and the carb in general looked good.  No varnish or discoloration anywhere when I open the bowl and the top..  In fact the pilot jet was clear.  I understand about tuning for mid or full throttle but I live in the city and so light throttle and liftoff is the order here and backfire is intolerable.  I am at 350 above sea level.
If you can please clarify, where does the replacement metal washers go?  I just replace the stock white one with the metal washers right?  Or some where else?
Thanks