Try a different mech squad. Blitzkrieg, for example, is vaguely similar to the Rift Walkers in composition but the mechs have much more specialized roles.

Random or custom squads also add a lot of diversity, though I do agree that Into the Breach doesn't have quite as much replayability as FTL with its greater element of randomness in encounters. I love Into the Breach and have played it a ton, but my biggest criticism is that the campaign itself doesn't provide enough variety; the individual missions vary from game to game but they are still a bit samey and there aren't any that stand out. I'm hoping there will be an expansion some day to mix things up a bit, either with some new mechanics or just giving us more islands and mission types.

Yeah, I feel the same. I felt way more attached to the runs in FTL and excited for every new game.