A micro-controller would be your cheapest and power friendly solution, shouldn't be too bad to program (if you have any programming experience). Avoiding the micro would greatly complicate the project, and use more power to run, but the care battery should handle it just fine, unless the other 7 function use a lot of power (loud stereo).
Since you have 4 channels, and only guessing that you can push two or more buttons at one time. You could actually control 15 functions, in binary, and fortunately there are logic chips that will take the 4-bit number, and convert it to 16 outputs. Pretty sure somebody has a part number handy. You don't have to use all 16, but might someday.
The push and pause method you want, would be much harder, but probably could be done without a micro, least for me anyway.