We are working on a game that might interest you. It's called Chezz and it's currently being soft launched on mobile platforms.
https://play.google.com/store/apps/details?id=com.quickbytegames.chezz&hl=en
https://itunes.apple.com/id/app/id1181015078
In Chezz, both players can play any pieces at any time but once you move a piece, you cannot move that specific one again until a short timer is completed. Check it out, let us know what you think!
Chess Variant Apps
jocly.com is the best variant site I have found so far. They also have mobile apps for both android and microsoft. They currently hold 115 games and at least 30 of them are chess variants. The rest are historical chess variants and other random games that are chess like in nature. My favorite is metamachy.
We recently released a free app for Colour Chess, which adds a new layer of strategy through a coloured board. The tabletop version won a 'family and education' award and was nominated for a Mensa award.
Your turn is in two parts: in the first part you have to move to the colour your opponent last moved to. in the second part you have to move a different piece to a different colour, that they then copy.
It creates a call and response game of sneaky structure disruption through forced movement.
Here's a new one that's really fun and challenging. http://www.verochess.com/