Aw, that's a pretty cactus. My first thought is no, do not remove anything else since there's been a lot of damage already. It may take a while for it to come back, so you just have to be patient. Even if it looks like it's not going to come back, I'd wait as long as possible. Since the root ball is intact, you've got a pretty good chance! I'd keep it protected, but make sure it gets enough sun. Scorching sun wouldn't be a good thing, so a happy medium would be best. Think of it as being in recovery, so no extremes, just limping along for a bit. Once new growth begins, you can make the call on whether to remove any of the old growth.
