I had an earlier problem with my k75 flooding and shutting off which I felt was resolved when I replaced the FPR.
Now the gine seemingly runs ok except for the somewhat rich exhaust and backfiring from time to time as well as the engine dropping to a very low idle after riding 20 or so minutes. I have checked the tps by disconnecting it but no change in performance. I have been through the gammit on this thing cleanig connections and replacing connectors, battery, temp sender, hall switches, spark plugs etc. I am missing something but I can't pinpoint it. It is very uncomfortable riding...lack of confidence!
HELP!! I am ready to sell this thing. I lost a summer of riding messing around!!

How did you adjust the idle? As this should be done when the bike is warm. So I wouldn't expect it to do so after 20 mins. Have you sprayed brake cleaner around the inlet stubs and checked the crankcase breather hose?

As Rene says a very careful check of all parts where air can leak in is vital and don't forget the little rubber throttle balancing stubs, the rubber perishes and a leak there messes up the mixture. I use carb cleaner as one needs something which is inflammable whereas nowadays brake cleaner over here in NZ is non flammable. A butane or propane gas torch is very good (unlit of course).
Regards,
K-BIKE

the worst culprits for leaks were injectors. The o rings perish with heat and either weld in the holes or just leak air. Don't forget to squirt some solvent or gas at the base of each injector.

Another thing may be leaking injectors... have you checked the fuel pressure? If not make sure the pressure hits 36psi and stays there for at least a few minutes after you shut off. Leaky fuel system can be a leaky injector.