Ok, I'd like to put a halt to the speculation:
1. I am still alive, and have not blown up any batteries or houses despite rumors to the contrary. Pirates and brigands have not overrun my car at an intersection nor am I running on LIPO, hydrogen, A123s, lead-acid, etc.
2. I am running two 15AH Ping 36V batteries in series, which as I count 'em makes it a 15AH 72V battery with a 40A current limit. I have room for two more such batteries to make a 30AH pack but have not forked over the cash yet. Yes, I will need that much battery for some long range trips.
3. I am running two motors with two 40A controllers (or at least, until a few minutes ago they were 40 amps....) A surge at the beginning of a throttle twist seems to be the culprit, overloading the PING BMS current limit.
Simple measures first! I took apart the motor controllers, and found the two shunts (quite obviously shunts, to my eye, pics to follow) in parallel. Snipped one shunt, and bent things to they cannot touch. Made a stab at a four wire ohms measurement and came up with 4.6 milliohms, about double the 2.21 milliohms marked on the controller. This measurement is at the limit of the equipment I have at hand, so it is not extremely accurate. Did this surgery on both controllers. This is despite John Robert's generous offer of reprogramming the controllers. He will get a crack at this bike soon enough anyway. He still owes me a wheel truing.
Hooked all the electronics back up to the bike. Voila! No tripping the amp limits on the BMS. I plugged an ammeter in where the battery fuse would go, and set the Cycle Analyst to 1, then 2 then 4 amps, and calibrated the CA milliohm shunt setting so my ammeter matches the reading on the CA within 5% or so. Then I set the CA at 15 amps, which seems to overshoot to 18 or 20 before it comes under control. Bike ran fine up on blocks, no matter how hard I crank the throttle. Took it out for a spin down the driveway (800 feet one way, a good test run) and it made it successfully. Climbed a small hill. floored it, never killed the amp limit in the BMS. Thanks to all who posted various solutions - I now understand some of the components a lot better, and have catalogued this issue for others who may run into it. next post I will show dissecting the motor controller shunts and explain four wire ohm measurements for any who are interested. .