You can fix the "desynch" by mashing the C button. Speed doesn't matter you just press it like 15 times or so. After that the Sonic icon in the life counter will screw up and you get into the next act.
But, you still need level select, as SYZ1 and SYZ3 don't seem possible to finish.
SYZ1 *might* be possible if you can bounce off every single enemy at the start to get over the ceiling, but I can't pull it off to see, even with savestates. SYZ3 is definitely impossible though. No way no way. :((
Every other level can be beaten, though doing most of them without savestates takes some serious balls.