What could cause unexplained brownout resets?
The H-bridge on the high-voltage side of the isolation stage had a very high slope when the upper transistors were turning off. Adding an RC-series snubber across the windings limited this slope, and moved the problem to where only one processor was resetting, and that at 95% of rated current. Doubling the C (further halving the slope) eliminated the problem entirely, up to 105% of rated current.

Conclusion: high dV/dt on a nearby converter can emit enough EMI to reset a processor, in a way that produces symptoms consistent with brownout.