My wrap puzzles show an infinite tiled grid, so there shouldn't be questions about which edge wraps where. There are no edges, tiles just start repeating after a while. Maybe I didn't understand your question about wrapping?
I have an idea of placing them with some kind of gesture - like touch and drag between tiles. That wouldn't interfere with tapping to rotate tiles. But on the other hand, I'm usually zoomed in on mobile and I use touch and drag to move around. Interfering with that would be bad too.
I'm open to ideas for better controls.