Another idea suggests itself: make the pieces entirely immobile on the
next move after a capture, but the piecces are self-readying: for
example, White captures a Knight with his Queen on move 28. The Queen
may not move or capture on move 29, but the Queen may move or capture
normally on move 30 or later.
If this game were played with thematic Kings, this could allow a King to
administer mate--if Black's King just made a capture, White's King
could move next to it and this is check and mate since Black's King
can't move and White's king can't be captured (if it could, the
checking move was illegal). Capturing with a bare King would mean
stalemate, as would capturing with your only mobile piece, if the
opponet's move did not release any other or oyur pieces.