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I think it would also be necessary (if we give black an extra move when capturing a piece) to ban him/her from moving the pawn which made the capture as the extra move. Also, black should be allowed to refrain from making the extra move if he/she finds it advantageous not to.
Given that we are experimenting here, probably let's restrict Black from making the extra move with the same pawn. all we want to do here is give Black nearly equal chances of beating White. Re your second point, fine (except that I believe that Black will always have space for an extra move). I suppose in the last stages, Black may be trying for Stalemate.