That adapter is supposed to help you set 0 offset. It makes a DC voltage of the 2 half waves which it adds and if centered would yield 0V on a DMM with that circuit. What I did was power the TT and look at pins 5 and 6 (I found it easier to clip leads on the E pins of the output transistors. Don't make the mistake that I did - running the turntable at an angle to get to things overloaded my transformer - and it effects these readings. So power on and set you volts/div to 100mV and make sure the emitters (5 and 6) both read 0. Then go to 1V/div and run the platter. The peaks should be 2 blocks above and below the center for 4V pk to pk. I slid the TT off the table to adjust these while running - one at a time.
For the speed adjustment, keeping to the higher time window (250uS and 550uS) is better I found. When running, the square wave on your scope should be pretty stable. This is the servo adjusting for every clock from the magnetic reader (284Hz). I couldn't improve it's stability adjusting gain or offset so I don't know if it's possible for it to be a perfectly stable signal.
My CX193 was bad and once replaced, I have WOW at 0.05% to 0.07% using the RMS WOW app. Speed was 0.07% accurate and slightly low on average. Moving the speed adjust to the higher end helped to increase the speed but there's a fine line to suddenly having the wave become unstable or it flipping upside down. It is a super sensitive adjustment. Seeing that it's so touchy and I had worn out the original pots with months of testing with a bad CX193, I replaced those pots and redid the speed adjustment. The new pots had much more friction which made them a little harder to set but I know that they won't move from temperature changes.
Can I ask, when yours is powered for a while, is the heat sink on the main power supply pretty darn hot? Like too hot to touch? (which I know for electronics is not a bad indication). I feel like there's not much in there to draw current to throw off that much heat. I'm all buttoned up and was listening to albums finally after 5 months. It's rewarding to have fixed it.