Spluttering/backfires on low throttle opening/struggles to build

There could be a few reasons for this but crank sensor sounds like it's breaking down when hot. But you would expect it to struggle to restart if it was the sensor, if it just struggled to tickover when warm the try cleaning the throttle body housing, if it ticks over really low you can drill a 1/8 hole in the throttle butterfly which just allows the idle speed control valve to operate in a slightly different position.

if there is a throttle body injection, one of the injectors may b stiaying open( exxes fuel in cyl)

blown head gasket

have you had the catalytic convertor back pressure tested. the symptoms you describe indicate a faulty convertor.

When you open and close the throttle can you hear the slide hitting the throttle stop?have you removed the slide, and fitted it in the reverse order, this would restrict full opperation of the slide leaving it in the part open position, the cut out side of the slide faces rearmost away from the engine, if you have exsess play in the cable at the carb, it is poss you may have fitted it wrong, unscrew the tickover screw almost all the way until you no longer hear the slide hitting it on throttle closure, start the bike you may have to hold the throttle at the desired revs, whilst doing this screw in the tickover screw until it just increases the tickover, you can now release the twist grip and addjust the idle to suite

Check for sticking idle air control valve and stuck open EGR valve. Both are common causes for very rough engine operation due to fuel-air ratio being too far off. Also check for large vacuum leak such as from rubber hoses connecting PCV valve to intake. Feel around for squishy or oily rubber which would indicate a leaking hole in the rubber hoses.

sound like the carbs need to be synced if throttle plates are fully closed at start it would cause a rich condition and no need for a choke becase there is very little air passing through mostly fuel if they are not eqaul there would be hesitation when opening throttles til about 1/4 throttle

Either take the carbs off and clean them or add some fuel additive to clean the system. Sounds like you have a clogged jet.

mate adjust the mixture screw on the carb to its correct setting in the manual and put the idle screw in a bit so the revs rise a tad good luck