Spray a tiny bit of starter fluid in the airbox while/before cranking.
If it temporarily starts,, your closer.
Ride safe, Ted
don't do that....

there is a port/passage way from the inlet side of the carb, up to the diaphragm... starting fluid and rubber diaphragm combo is not conducive to happy outcome. spraying anything flammable in an airbox ain't either (not ether..hehheh pun)
the filter catches it, and holds it.. and if it pops and backfires...

oh... sorry, I missed the part about no airbox, and individual filter pods...

well, that just adds another variable to the cake.

there is no shortcut to cure blocked starting and low speed idle circuits in these carbs. It requires disassmbly, and complete cleaning if the circuits feeding those 4 little holes that sit up under the butterfly throttle plate..
and so far, there has been no mention to what decade vintage of turpentine/fuel is sitting in the tank... which should be the FIRST thing to dump, clean, and replace with fresh fuel from a clean container..
the "sticky" enrichener lever incident should be an indicator, the levers themselves really should not stick, but if the other end of the enrichener, the actual pistons themselves, are glued in place by gummed up old syrup, they ain't working either.. this can be easily seen by attempting to move the slide bar manually by hand, where the cable attaches to it.. all these "symptoms", when looked at with perspective, are very indicative of the gummed up shape the carbs are in.