I've done a couple of these and am about to do another one on my mill.
Flywheel vs. no flywheel - the flywheel provides cooling and rotational inertia, so if you take it off you'll have to fashion a replacement fan and the motor is more likely to slow and surge under interrupted cuts. I tried it and ended up putting the flywheel back on.
Poly V vs. A section V belt - I've done exactly as suggested above, cutting the Poly V part of the flywheel down and then putting a small V section pulley on. I used a home made arbor to mount the flywheel to the lathe. I used a set screw in the pulley for added insurance, then mounted the whole shebang (rotor and flywheel) between centers and trued up the pulley to make sure it was running true. Didn't take much. One big tip though - use AX cogged belts. Because treadmill motors run at ~4000rpm full speed, you need the smallest V pulley you can get on there and AX cogged belts cope better with smaller pulley sizes. My build should be on here somewhere under mattthemuppet username.
I've also used the poly-V flywheel as is by mounting the matching poly-V pulley off the roller on the countershaft of my lathe. Works REALLY well with no slip whatsoever. I'm in the process (much delayed) of making poly-V pulleys for the countershaft to spindle. I've made the countershaft poly-V step pulley, just need to make the spindle one, which is a fair bit more involved!
for the mill, I'm going to make a stub adapter to attach to the poly-V sheave so I can mount the original step motor pulley, but at some point in the future make a poly-V pulley to mount to the idler pulley.
for preference I'd use poly-V belts, but for convenience the V-belt approach is a lot easier