You can watch the floor lever flopping around, and there are rub marks where the transfer case has struck the cab. That is very indicative of worn out drivetrain mounts. They may well appear fine to look at them, but from your description they clearly are allowing too much motion. The transmission mount does little to control torque, that's the job of the engine mounts.

Clanking going between reverse and forward gears is not uncommon in really any vehicle as slack is taken up in the driveline. The ring and pinion gear of the differential give the most play.