B/C Ttar or SD/SE Ttar?

Charged TM SD/Crunch to SD/SE.

None of these need Fast TMs; if a Ttar has Bite, CTM to Crunch, and if it has Smack Down, CTM to Stone Edge. I would also power up the 2713 from the trade, especially if that's a 96% with a 14 or 15 in attack.

SmackDown is an exclusive move and can't be obtained later on. Better keep smackdown on that tyranitar and change the charge move to StoneEdge.
Bite and Crunch also works together.

in the end
3478 / 98 - B/C (tm away SE)
3330 / 81 - SD/SE
3021 / 93 - SD/SE
2714 / ** - SD/SE (tm away C)
2713/96* - SD/SE (tm away C)

you can get Dark Tyranitars anytime later on if you want to balance them out.

for power-ups, your bite Tyranitar(3478/98) and new shiny one(2713/96*) looks ideal

Keep all smash down for a double rock set

I'd power up the bite crunch one first, if moltres does have a raid day, its double weakness to rock will mean tyranitar wont need to be super high leveled to dent it substantially, however if it is partially cloudy in your area a lot, you may want to power up ypur best IV smack downer. However you will be wanting a lot of bite crunch ones for gen IV, Giratina and all the psychic types, as well as the EX mewtwo raids, and while Celebi is the next special research, I think its somewhat likely they will release mythicals in raids as the number of them is getting higher, and both gen III ones are weak to dark

I missed the larvitar CD and have none with smack down, and here you're talking about TMing it away?!