Admittedly I'm much more familiar with the operation of slide carburettors, Dell Orto and Amal, but nonetheless the main jet shouldn't come into play until around 3/4 throttle opening. There is no way that's going to happen on a stationary bike. It worked before and it doesn't now. I'd be inclined to look at what has changed, starting by putting it back to stock. If the fault goes then it must be something that was done to it, if it doesn't then something else is to blame. I used to run a 900SS with open airbox and pipes and a Factory Pro kit. It ran very well indeed with a 140 main jet (OEM fitment), the Factory Pro needle in the 4th notch from the top, 42.5 pilot jets with the screws 3 turns out, the supplied Factory Pro springs and the floats set to 14mm as advised. This of course was a 900 and I'd expect the jetting to be different for a 600. The OEM fitments for the 600 are 132.5 main and 40 pilot jet. It seems the 900 at least was jetted rich from the factory if the same goes for the 600 then a 132.5 should be more than adequate for the main jet. Although I think that chasing main jet sizes is a waste of time. There might be a problem with the air cut-off diaphragms but I'd return every this to standard first then make one change at a time. If you keep meddling with one thing after another you have no reference to go back to.
Double check the floats are set correctly for the bike, make sure the float valves are properly clean and open/close cleanly, they need to be carefully inspected for stuff getting stuck inside the valve seat. Try running the engine with the fuel tap closed to see if the running improves as the float bowl empties. The symptoms described indicate far too much fuel in the float bowl to me.
