I figured I'd post a follow up. The LSD shaft ended up going back into position inside the differential with only firm hand pressure once it was lined up perfectly straight. So no hydraulic press was needed. I refilled it with Haldex, tipped it in every direction possible to check for leaks, and finding none, carefully reinstalled it in the car. After about 10 more attempts, it did finally go on flush with the transmission as it should. I guess it just had to be lined up perfectly. I bolted it on, attached the axle and all the intake parts, and took it for a ride. Clutch felt stiff and the friction point was very close to the floor, but they have both already improved over the past few days. I tested the diff by stopping on a hard pack snow patch with one front tire and the other on dry pavement. Then, with traction control off, I took off fairly hard. The diff did it's job and the pavement tire grabbed hard to launch me forward. I'll wait a couple hundred more miles before pushing it hard.
So everything works as it should. I'll periodically check for Haldex leaks, but I'm feeling pretty good about it. So thankfully it only cost me one extra day of worrying and no extra money. The only tools I had to buy to do the job was an engine support bar ($80) and a 12-point 9mm socket ($3) to get the stock pressure plate off. Otherwise, I am happy to say I replaced my stock clutch with a new Sachs Performance clutch and upgraded to an iAbed RMS in my garage on jack stands. It took me about 12 hours over 3 days, but much of that was me taking my time and cleaning every part that came out before it went back in. Plus lots of extra time because I could never find the right socket/adapter when/where I needed it. Does anyone need an engine support bar? Hopefully I'll never need mine again.
Thanks again to all of you who gave me advice.