You have an excellent setup to test any motor at no-load with an supply voltage up to 90V.
I hope that you don't mind if I make some suggestions and comments about the test.
1) "The current limits on the PSUs keep triggering - this alone could invalidate any results"
What are the current limits used?
Would suggest to be about 2 or 3 A for no-load test.
There is one main difference between battery and PSU. Battery could supply current (forward current) and take back current (reverse current). PSU could only supply current but NOT take back. There could be some "reverse current" from the motor. These PSUs could be too sensitive to the reverse current.
2) Use the lowest supply voltage to determine the best combination for the forward. The best combination will give the minimum supply current. The supply current could be read in the PSU. In your case the lowest voltage is 36V for this controller.
3) "I solved the sensor/winding wire puzzle by trial and error (OK, I did use advanced mathematical techniques to make sure it took only the minimum number of trials)."
Noted that you have already achieved this by trial and error.
4) "I am using 3 PSU's in series to make a source that can be adjusted up to 90 V. Look carefully and you can see the diodes strapped across each one. "
How did you connect these diodes?
Are these diodes are connected in reverse and across each PSU?
5) "There's a lot of noise on the signals, so scope triggering is an issue. Noise is much worse at partial throttle."
Try to use one channel to measure for one certian Hall signal and only use this channel for triggering.
Then use the other channel to measure each of the other Hall signals, motor phase voltages ( one at a time) wrt the -ve of the supply (as close to the controller as possible).
Measure also the time period for 1 cycle of the Hall signal and its frequency could be calculated from its time period. The frequency of motor phase voltage is same as the Hall signal.
6)"BTW, its a geared motor with freewheel. Don't know if this is sad or what, but I just put a counter on one of the Hall sensors and turned it backwards one turn. Keep getting a count of 86. For some reason I was expecting it to be a multiple of 3, but I don't suppose it has to be anything special if its geared."
How did you measure?
A simple circuit as suggested in the attached picture could be used to measure the Hall signal from one sensor with counter.
It uses one 5 V supply , pull-up resistor of 2.2k and simple noise filter of 3.3k and 0.01uF for the countor.
No of counts for 1 turn = No of pole-pairs X Gear-ratio
If this motor has 10 pole-pairs and gear-ratio of 4.3 (this data 4.3 was mentioned by Knuckles?)
Then no of counts for 1 turn = 10 x 4.3 = 43 counts.
If your counter counts the edge of rising and the edge of falling as 2 counts, then the number will be double .
7)"For some reason, the system won't let me get above 71.9 V. If I try to push it, the noise changes slightly."
Did you note the frequency at this instant?
It could be the same critical frequency as observed by fechter.
"What I do have is breadboard dc-dc step up converter that will make hi V from a car battery. I've only run it up to 80 V so far, but there's more there. "
What is frequency at 80V?
Would like to see the voltage waveforms on scope for full throttle and partial throttle.
Especially at partial throttle to see if the phase voltage is symmetrical or not.