Nightmare, just paid for the new battery and I still have the exact same issue.
What next? I assume it's either a wiring or controller issue.
Remember way back, you measured the cell group voltages, and there was a standout bad cell group?
That was a genuine battery issue, the controller etc cannot make that happen. A defective BMS could, but nothing outside the battery can cause that problem.
So: new BMS fitted? If not, suspect the old BMS. If yes, then either the new battery also cannot handle the current because the demand is so high, which is just a parameter of the motor, or there is a problem with the new battery.
How to tell?
1. Fully charge battery and run around really gently until flat. I.e. treat it gently, low current, and see what range you get. Or,
2. Get one if those cheap wattmeters and set up a discharge test rig, and do a full discharge at about 1A, and see what capacity you get.
3. If all points to a battery issue, open it up , test the cell group voltages, and so on as before.
My guess is that the battery cannot supply enough current when you use the throttle and it is under 60% charge, so the voltage is pulled down to the BMS cutoff, so it cuts off. I think if you open up the new battery, assuming it has a new BMS, the balance will be fine, but the cells are just not capable of sufficient current delivery. That is not necessarily a cell problem, so much as just a very demanding type of motor.
If that is so, nothing for it but a massively expensive battery or chuck the motor.