Posting an update.
I replaced the clutch with an Exedy Organic clutch (From ProStreetonline - have to support the sponsors

, plus it was a great price

) The clutch was certainly the problem. A piece had broken off the clutch plate, so it looks like only half the plate was disengaging from the flywheel. Luckily, it didn't damage the flywheel considering the size of it. Here's some pics:
Clutch plate and broken piece
Close-up of broken piece
Damaged Springs
Pressure Plate
So shifts are again smooth, but I now have to get used to the stiffer clutch pedal of the Exedy.