So if the ESC problem is eliminated, the simplest and proper solutions is to sent that timer to me, I can measure it all.
BUT ... if you want be sure that accelerometer is problem, simply set sensitivity in timer to 0 and test, if it works on costant speed properly all the time, it is the case.
However from what you described, the problem is somewhere between timer and ESC, cable or connector. Such behavior can happen because ESC has some kind of "elongation" of lost signal, means if timer fails and stops sending signal, ESC will use last for 1 or 2 seconds. So it looks like broken connector between timer and ESC. If it is new timer with replacable cable, try new cable. If is old, better is to send it back to me.