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If it's firing on 1 & 2, but not 3 & 4 I'd say it couldn't be the petcock. The 1982 carbs just have the one fuel pipe on it right (I have a 1981)? I recall some of the SOHC bikes had a petcock that split into two hoses so fuel entered the carbs from 2 locations.
My vote would be that it is a compression issue. If you have zero compression in 3&4 then fuel can't be sucked in. The compression test will tell you.
Carb swap will not fix this, unless your old carbs are in bad need of cleaning, but since you've cleaned them 7 times this shouldn't be the case.
Just to be sure, can you elaborate on how you cleaned them? A simple soak/ultrasonic often isn't enough for these carbs.
Probably unrelated to your starting issue, but those are some big jets, so I'm assuming you are running fairly open pipes and pods or velocity stacks. These carbs are notorious for being difficult with anything other than the stock airbox. I would focus on getting the bike running well with a fairly stock set-up, then start messing with pods etc.
Another aside - if you're going to run the GSXR carbs, how are you planning on making them line up well? I'm interested in this mod myself, but can't seem to find a good manifold solution.
Edit: I just did a quick search and I believe that the 36's are going to be way too big. The appropriate Mikuni's are the 29's. That said, don't take my word for it.
1981 CB750K with 900 cams
90K KM's, rebuilt head, rebuilt carbs, upgraded valve stem seals
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Strawberries for supper. Yes, I am a lucky man.