The single wire serial requirement considerably increases the complexity and cost. For single wire serial you'll need two uCs (with at least 16 I/Os and, of course, the necessary code for both).
If you're willing to use a shielded 4 wire cable (standard indoor telephone cable, for instance, shield as ground) you could use one Sparkfun 9056 to mux the touch screen signals, xmit the binary output (s0 -> s3) to another 9056 (in reverse) to demux for the 16 control function(s) you want.
No doubt some manner of current handling circuit(s) would be needed at the output end.