Great info on this thread. Let me add a tiny bit more. This from my Rotax guru in Marin County.
During a discussion about why i'm not getting decent EGT at 5600 rpm with my present prop (Culver 60x28 on a Rotax 277), he explained why my EGT will go up if I prop the engine to reach 6200 rpm.
I'll paraphrase as closely as I can: "it seems counter intuitive, but a 2-stroke Rotax will run richer, thus achieve a lower EGT if it's over propped. Here's why: the cylinder displacement defines the volume of air drawn per stroke. For a slide carb, this means that when your slide position is higher than it should be because the engine is trying to accelerate. The amount of air drawn per stroke will be the same, but because the needle is up higher than it otherwise would be, more fuel will be delivered with that air, thus the engine runs rich. Now, if you prop correctly, that same rpm will occur at a lower slide setting, and the engine will be running leaner. Further, at wide open throttle, rpm will be better matched, and you will be in the power band with maximum HP and appropriate EGT - 1100 being about ideal."
Wildman's statement #1 above may be correct for 4-stroke gas or diesel engine taking dynamic data on a dyno while accelerating to rpm, or loaded to drop rpm, at WOT. That's not how a 2-stroke would be tested...it just wouldn't make sense because the engine wouldn't run right.
Statement #3 is very helpful, and explains why my 503 would run away from its propeller - it was propped as an aircraft engine, but was a snowmobile engine capable of more power. Very interesting. Amusing, even.