Rather than keep trying I plan to re-cut the piece.
I'm glad that's an option for you as it's generally the best course of action in such a situation. Although sometimes one can remove warp successfully there's no guarantee it won't try to return.
Anyone have any suggestions on how I can keep it from developing another twist as the wood dries out after cutting?
Wood shouldn't be expected to twist after cutting to size and surfacing. What I mean is that twist isn't inherently a risk with every piece, it is generally down to the individual board. Pieces with swirling or irregular grain are good candidates for a greater likelihood of twisting; but boards with reaction wood somewhere in them are as well and this is harder to spot1.
Other types of warpage however are to be expected with nearly any piece of wood. Almost any board of sufficient size will try to cup or bow slightly, if stored poorly..... and just laying a recently planed piece flat on the bench overnight is poor storage, despite how commonly we all do it!
Select your wood with more care.
Store it more carefully after processing to shape.
If you're doing more than just skimming the surface to clean it up, don't just process it on autopilot.
Pieces with fairly consistent grain, boards with rift-sawn or quarter-sawn grain orientation and straight-grained pieces are inherently much more stable than those with irregular or wild grain (as attractive as they might be). That's not to say you can't use wood with wild grain, but you need to be more careful with it.
As mentioned above, just laying a piece down flat on the bench (or any flat surface, including the floor) is bad shop practice. Ditto leaning against the wall. Both of these are OK for stuff still in the rough (we can do better) but after processing you should take more care. Either sticker the pieces and put weight on top, or wrap well in plastic. Refuse sacks/bin liners are great for temporarily wrapping wood while you're doing other things2.
When you're going from rough-sawn to smooth, or reducing the thickness of a board substantially, ideally remove material equally from both sides. If you think the wood has potential to distort (and in your case this it is probably a safe assumption that the next piece may be similar to the first) another safety step that's sometimes taken is to remove material in stages, letting the wood rest for some hours or overnight in between to allow it to move a bit. The idea is that any small distortion will be taken care of during the next stage.
1 It may be identified by tightly packed grain in some places and more widely spaced grain elsewhere.
2 And the wood can safely be left bagged for extended periods of time. So if life gets in the way or you just lose momentum on a project don't sweat it, as long as the bag isn't somewhere which experiences wild swings in temperature.