The problem is that I couldn't get it aligned perfectly with the transmission jack, and then didn't have enough strength to wiggle it in if I lowered the jack out of the way a bit.
A friend goes a long way with this job. First, holding up the rear hubs while you slide the axles out, then removing the transmission, and finally, re-assembly. My wife helped holding the hubs, but the transmission alignment was a little tricky.
While this took about a week fiddling around with the reinstallation, it mostly sat until I could have a buddy come over and help. I really only spent about 30 minutes total trying to wiggle it in myself.
Now all I have to do is torque the axle nuts to 240 ft-lbs and stake them, then start it up. I'll check the clutch pedal play later.
For those of you that have the '02+ headers, be very careful tilting the engine down to gain clearance: I damaged the rear O2 sensor because it hit the vertical "A" brace while lowering the engine. I bent the metal sheathing around the wires. The wires look OK, so for now, I'll see if it throws any codes or has the stumbling issue. Here I was worried about stressing the three main coolant hoses as I lowered the engine, and didn't notice the O2 sensor was rubbing.
The newer Exedy twin organic HMG12SD clutch is about 25% stiffer pedal feel than the OEM clutch and the RPS twin carbon I just removed. Some extra pedal effort was expected with a stiffer pressure plate to hold the torque, and it seems liveable. The clutch pedal moves sooo smoothly now. It wasn't bad before, but this is really nice. Even though I ran it through the gears while the transmission was on the ground, it was a nice feeling that it seems to work OK installed in the car.
Hopefully the roads will be dry this evening to take it for a test spin. Thanks again everyone for the help and encouragement. I still prefer tearing into an engine than a transmission though.