Things to check:
So we need three things for the engine to run,
Timing of these is essential and the assumption is that the timing is correct.
Sounds like you have two of three, air and spark however the fuel seems to be restricted. From the description it sounds like the engine runs until the fuel in the carburetors is gone then a trickle of fuel eventually fills then up over time.
Check that the fuel line flows enough fuel to keep up with the needed.
The most likley cause of your problem is that the radiator fan is not running or turning on. Easy to check, run the bike untill the coolant bubbles out and listen for the fan. If you put your hand in front of the rad it should try to suck you hand toward it. If yhe fan is not running than you wither need a new fan or coolant temperature switch for the fan. It should be located in the head of the engine.
The internal design of a motorcycle ignition switch is typically complex and often is at least two independent switches working together. Where electronic immobilisers are concerned there is sometimes an in-built resistance the system must "see" before it will work.
Bypassing the switch safely would not be easy even with a wiring diagram and truth table and I suggest you don't try.