@XJ12 - I pulled up the tech manual/wiring diagram. It shows the two power pins in the J1772 as being fused at 50A... so I'm not sure that tells me much but it does leave open the possibility that it could be engineered for 40A sustained... which I would probably read as occasional extended peak draws of 38A, assuming one derates auto fuses the same way one derates building wiring/loads.
@daveo4Bolt - noted, and there's a reasonable argument to be made that it's costing me more to think about this than pay the differential for 40A. The pedant and engineer voices in my head, however, are carrying the day.

Your point about the subpanel is excellent - that is in fact what I had planned to do.
@DucRider - I looked into DCFC for the house but a) it's such ludicrous overkill that even I can't justify it even if it wasn't $10K, and if I recall they mostly require 3-phase service, which I don't have. I will be upgrading the house's 60s-vintage 150?A service to 400A, to clean up some legacy / maintenance issues, pull 100A to the driveway (for future 2nd-driver EV, and hopefully later a detached 2-car garage and radio tower), conversion to all-electric appliances to work towards carbon-neutrality), add backup generator hookups, etc. I asked the power company what 3-phase would cost me and the answer was "at a minimum, cable costs from the nearest point where it's available to your (end of the line) residence". So I think L2 is about my speed for now.
After 30 minutes on the phone with GM corporate and a very disinterested (and uncited) statement by technical assistance that 32A is the max it'll draw, I'm tabling this. I plan to install a 100A subpanel with a 50A breaker/weather-proof outlet, and a 40A EVSE for starters. Then I'm going to see if I can catch it pulling more than 32A (battery conditioner running, cabin heater running, ham radio amp drawing, who knows what.)
Documenting this for posterity in case someone else (or future-Watts) finds actual engineering citations for what/why it can/not draw more than 32A.
Thanks to all who replied!