Rounding this off, I bought some 3S batteries to go from 12S to 15S and it doesn't work!
The spec for this controller is 48V nominal, 60V max. With 15S connected up (60.5V measured, not fully charged), the controller makes the normal spark as the caps charged, it makes its normal faint whining noise, but no response to the throttle. Reconnect as 12S, everything works, re-reconnect at 15S, not working again. I guess it's a high-voltage cutoff, and when they say 60V max, they mean it...
It's a shame as 12S isn't quite a good match for this controller. It seems to have a smart LVC, in that the lower the pack voltage goes, the lower the current limit becomes. I suspect it current limits to keep input voltage at or above a LVC threshold. On 12S this means that by the time you get to 3.5-3.6 VPC (resting) the power limit is about 300W. Fortunately, I don't normally drain it this far, but in the winter when the batteries sag more it becomes more of a nuisance.
Next upgrade is 18S and an 18FET controller.