The problem is that I can't understand what you're telling me, though it sounds like you have some dodgy wiring.
You still didn't answer my question about whether you have a speed sensor on the wheel. You have a Cyclamatic motor that doesn't have a speed sensor in it, so this is an important question. It's not normal for speed to come and go by itself unless you have a wheel speed sensor that's not properly aligned with the magnet, but if you don't have one, we have to ask where your controller gets the speed from and why it comes and goes.
If I had your bike in front of me, it would be fixed in 5 minutes, but I'm really struggling to understand the facts. Post #14 was very good. I've got the overall picture.
Please answer the question about the speed sensor then answer this one:
Fully charge the battery to 42v. Set the LCD to read battery voltage by short press of the power button a couple of times, then read the voltage and write it down. Lift the wheel off the ground and power the wheel like before while you observe the voltage. Describe what happens to the voltage during your observation.