Adam, I am not telling you to turn on trace flags or modify your app server logging.
I don’t know all the implications of it, but I know* someone from Epicor support or another power user here could help answer what tracing affects performance and which traces don’t. I know I have been verbally told this info several times, but I never retained it.
If I were you, I would play around with it on a test app server (if you have one). See what happens when that BPM runs, see if the app server logs anything useful. Maybe it could help you get to the bottom of it the next time it happens.