Washing Machine randomly shuts off mid-cycle

My Whirlpool washer (Model #LSQ7030LQ0) randomly quits, not always at the same exact point, during use. At first, I thought the lid switch that I had replaced a few months ago might be defective, so I installed a bypass wire on the lid switch plug; but that didn't solve the issue. I had the motor start capacitor checked out by a local guy here, and he said it registered the correct reading (micro-farads). So, I did a little asking around + a little internet research. My wife said she had smelled a "burning" odor a couple times just prior to the machine acting up, so I included that in my research. The most likely culprit, I was told, was the main motor. So, I got a used one on eBay and installed it this morning. The machine fired right up and got ALMOST all the way through the first load of clothes... it conked out just as it had filled the tub up with the final rinse water and was about to click over to the "high spin" and finish up. I can usually unplug the washer when this happens, leave it for a while, plug it in later on & successfully finish a load, so it's not completely dead. Something seems to just be overheating or something... Any suggestions? Perhaps the timer? Obviously, I'm trying to NOT get into a guessing game and throw a bunch of parts at this thing. Even with buying used parts, it gets expensive real quick. Thanks in advance for any assistance rendered!