took on the Elite 4 with my new team in this playthrough.

Mega Gardevoir one-hit KO'd everyone. :(

I think trying to hatch for a shiny Larvitar is holding me back from trying to breed other Pokemon. I think I should stop and just use a Larvitar already.

Ancient Power isn't one of Swinub's egg moves. You have to get it through Move Relearner as a Piloswine.

Huh. It used to be...

Should I chain-breed Freeze-Dry into a Swinub to cover the 2x Water Weakness?

Moves change (Nosepass had Head Smash as an egg move, but had no breeding partners who could learn it, so the move was completely removed from Nosepass's move list, for example)

For Freeze-Dry, I don't recommend it unless you run a mixed set on Mamoswine.

Mixed set?

Physical attack and special attack

Yep. Mamoswine has 130 physical attack, 70 special. With Freeze-Dry being a special attack, you'd have to be running a mixed set to pull it off.

And given the difference between those two stats, physical attack is the way to go

In light of recent information, Brynhildr the Mamoswine not Stealth Rock since Stealth Rock is unlearnable in Gen6.
Any suggestions for the last move slot?

Also, Jolly or Adamant? Eh, I'll make one of each.