You don't eliminate gerrymandering in that way. You limit it.
STV works best in limited magnitude districts (three or five seems to be preferred) or else the number of options becomes too difficult for humans to express a coherent useful and accurate set of preferences. Once you limit magnitude, you can draw your districts to benefit you. For instance, perhaps you'll discover a preference for two or four seaters in reasonably strong Democrat areas and three seaters in reasonably strong Republican areas. You need fifty percent plus one to get a majority of seats in an odd numbered district, but fifty percent plus one only gets you fifty percent of the seats in an even numbered district. I can imagine Americans spending huge amounts of political capital for years getting STV in, only to discover that one party still has a manufactured majority because they wasted votes efficiently.
Its true that gerrymanders per se become harder and harder the higher the magnitude, but if your problem is you have a political system that is opposed to hearing the will of the people they're going to find a way to stuff their ears no matter what voting system you pick.
(Aside: Open list PR is both candidate centred and party-list. You vote for Fred Nurk of the Purple Party. That helps the Purple Party win more seats, and it moves Fred Nurk up in the list. It seems to be the only tick-a-box election system which doesn't devolve into FPTP in a district magnitude of 1 so it might be appealing in the US, where several states only elect a single representative. e.g. You vote for Gregory Hsien of the Maroon Party, who stands in a group with Josephine Yusuf of the Red Party. The Red-Maroon group win one more vote than the Blue-Cyan group even though the Blue party got more votes than the Red party. Reds win because you voted for their ally, the Maroons.)