I know this is Hybrid Z, and I try to cut them up with the best of them, but a V8 and widebody on a solid Series I 240Z when you have two later cars sitting there, ouch..... I must be getting old.
Anyway, be careful, as you have found, the tranny mount is the third leg of the tripod that hods the engine and tranny in, it falling like that is normal.
If you are only wanting to do a 5 lug conversion with the Z31 suspension, the front hubs from a Z31 will actually bolt on a first gen. Z's used the same front wheel bearing diameters until 89. You can then use Toyota truck calipers for a brake upgrade too. The rear is a different story, you have to get more creative or spend more money at that point.
A friend of mine did a 280ZX t-top conversion on a first gen, it is nice, but he and the body guy said never again.
Good luck,
Jason