727 TC Installed - Probably Wrong...

I think I will have to disconnect the trans and TC again unfortunately.

Then I will confirm the engine turns over freely by itself, which I have not had a problem with yet.

If my understanding is correct, the TC should rotate on the transmission shaft when it is fully seated. Is this correct? Does it matter what gear the transmission is in?

Both should turn independently before bolting up the TC. Gearing should not matter, as it is hydraulic, and there's no pressure. This is why you cannot push start most modern automatics.......only the early ones with a rear pump, which is spun by the driveshaft