Upon reading the “oh noes” at the top, it looks like the ADC FIFO can’t be read fast enough, which would make sense since the signal was so fast. Would a better approach be to send a warning message to the user “Warning: ADC FIFO has overflowed. Output may not be accurate”, rather than forcing a restart?
If this was your plan but you haven’t had time to implement it, I might be willing to help you out with that. I have a bit of experience with TI’s LM4F series of M4 chips, so I ought to be able to help out some with an M3.