Yes there have been pilots who transitioned from pistons and king airs into the left seat of a Lear 20. It is interesting to sit in on their first recurrent. There are some interesting stories. Most insurance companies want to see some Lear experience before becoming PIC.
In the 20's if you fly fuel flow rather than speed, you do much better. As for flaming out, the engine sync or speed has little to do with it. usually it is caused by a FCU misadjustment. Many operators do not know or are unwilling to do the required maintenance check called a burst test after they change a FCU or engine. The Mark II wings' recommended climb speed is .70m. However, above FL350 it does climb worth a ****. It does much better above .74m.
Going from a 35/36 to a 20 is not too bad. Just have to get use to the fuel burns. But a 31 going to a 23/24 with no experience in the 20's will make for some interesting times.
As for taxiing on one engine, if you planned the fuel that tight in the first place, you probably shouldn't be doing that leg. Also some of the early aircraft have steering that really doesn't like working when taxiing at high weights on one engine.
Personally, I believe that RVSM for the 20's is a crap shoot. Until it gets certified, you don't know if it will happen or not. Also the price will not be firm until it is certified and the after the first half dozen or so roll out the door. The early aircraft, I have been told will most likely need a new autopilot. Time will tell. But most operators who are buying 20's right now are treating them like throw-aways. If RVSM haopens Great. If not, the aircraft paid for itself.