You're absolutely going to catch HELL trying to mount the transmission if the engine isn't mounted.
I swapped my transmission the first time with the TCase installed, and that was hell in itself.
Second time was a breeze with everything unbolted, and just installing the transmission.
If you've got driveshafts and everything still attached, Engine just free-swinging from a hoist/etc, I completely understand now why there's an issue.
It's finnicky. You've got about 1" of lee-way for it to connect. Any additional angles or extra oddities involved are just going to delay you further.
As far as the stripped Skid Plate bolts, they're nutserts, I'd bet they ARE stripped, they're practically irreparable, and replacing them SUCKS.
I used a cutoff wheel, and "X" scored the nutserts, then punched them out, grinded everything back flat, polished with a flap disc, and reinstalled new ones.
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@mrblaine sells a kit on Black Magic Brakes. Pair that with his Nutsert Tool.
It makes the headache a little more tolerable.
Also to note, I would be extremely hesitant on NOT replacing the nutserts, depending on how many are stripped.
They're the only thing holding your skid-plate on, and the skid-plate is the only thing holding your transmission.
Drop a skid plate, and the guts of the jeep drop with it.
Best of luck to you!
You're in something I like to call a "shituation"