So... I've had it running now for over 3 hours without crashing. Here's what I found.
BigBox was running under PageHeap / IFEO debug instrumentation, which was making it far more likely to terminate or behave abnormally during long runs. Windows had a hidden per-app debugging setting attached to BigBox.exe, even though normal verifier /query looked clean.
BigBox itself was being destabilized by PageHeap being enabled, and removing it fixed the problem. The crash problem was caused, or at least heavily triggered, by hidden Windows PageHeap debugging being enabled specifically for BigBox.exe.
- This may return or may not have fixed everything but I've not had it run for 3 hours for at least a month.
-McFly-'s post in Launchbox crashes / hangs with too many platforms. was marked as the answer