First, I'd like to add a few things to your comments and analysis:
There is a hell of a lot more to measuring the latency between the tactile input and what your eyes perceive.
Probably the biggest one I'm seeing missing in your tests is the latency between the graphics card and the PC monitor you're testing on. Many common LCD monitors these days have a latency of between 15-30ms in processing lag. I don't know how much this relates to mobile screens and hardware, but I would suggest you take the time to perform additional tests on your target hardware before drawing further conclusions.
To more directly answer your question:
I would continue to use Unity however I would continue to research the best methods of taking the input and feeding it back to the player as fast as possible. In the above comments @rutter has pointed you to what appears to be a pretty good thread on the issue.
Of specific note I would look at using FixedUpdate() to decouple the framerate of the game from the input processing speed.
I think it is also worth putting time into researching the psychology of the perception of latency. For example, if your game is a sort of Guitar Hero game of matching the playing song, you could simply take into account the lag you know is there and in your game logic take that into account when checking input.