[hbskhzci] Anti-mirroring Misere Tic-tac-toe

In misère tic-tac-toe, the first to get three in a row loses. The drawing strategy for the player moving first is to play in the center, then play symmetrically across the center from each Player 2 move.

Cosider a variation in which, if the final position is point symmetric in this way, that is, Player 1 has marked the center and all pairs of opposing squares across the center are of opposite colors, then Player 1 has lost. We penalize the mirror strategy, even if played indirectly. Who wins this game?

If Player 1 does not play in the center on the first move, then I've heard Player 2 can win (i.e., force Player 1 to make 3 in a row). I don't know if there is a simple strategy. This might be an interesting variation in its own right, with draws counted as a first player win.