Took the opportunity to instrument the machine last night - wasn't able to find any issues or bottlenecks on disk. Specifically, I couldn't find any correlations in queue length, latency, or %active time and the Warnings the server kept throwing. Like I mentioned above, the disk (which is dedicated to this application) is on a pass-through to two small SSDs, not being shared or virtualized. So while it was a good starting point, I don't think IO is my issue.
Anyone else experience this?