Update...
I don't know how to edit or delete post with these forums.

I got the starter to engage "properly" and start the car by adding a washer to just the upper bolt. Apparently, this gives it just enough of an angle to clear the flywheel. I'm assuming the flywheel was just a little out of spec? I know it couldn't be my fault.

I even tried calling Clutchmasters this morning and they said they never made a steel flywheel. It had the part number FW-1922-Steel on box, which matches for the Neon. So I went and picked up a new starter before I tried the washer thing. Luckily it just wouldn't fit because of a coolant pipe, or I would be out another $120.

The only thing I have left to fix is the ball pivot thing that clutch fork rests on. For some reason its made of plastic, and I smashed it throwing the tranny around. Does anybody know where to get one?