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Here's another chess variant that I invented that does not resort to using
Shogi-like drops, and which may also be computer-resistant to some degree;
however I have even more doubt than in the case of Sac Chess that this
variant will ever become popular:

http://www.chessvariants.com/index/msdisplay.php?itemid=MS4chessfourdime


Then there could be Crazyhouse (or even Bughouse) versions of the following variant of mine (which is similar to Grand Chess); such a version with drops might prove computer resistant to some degree (drops might be limited to one's own half of the board if necessary, to curtail an engine's ability to forsee mating sequences with drops, if the game would then still prove playable). Such a variant might even have a fair chance of becoming popular someday (pawns could be prohibited from promoting somehow, e.g. like in Australian pawn rules Standard Bughouse, if that helps by removing the need for another set in over-the-board games):

http://www.chessvariants.com/index/msdisplay.php?itemid=MSchess1010