Ok! I've found a cause. For some strange reason, DP was having some very weird sample rate mismatch.
I only found it because I enable the 'Project Settings' option in the transport. This is what I saw:
The project was playing back audio fine. Soundcard (either RME Fireface or Saffire Pro 40 stack) was showing the correct sample rate.
I sent a project with this issue to 5 other people, and they all had the same quantizing issue. So it must be some weird project corruption?
How to fix it:
1. Open a project with the issue.
2. Go to Setup->Configure Audio System->Configure Hardware Driver
3. Set the sample rate here to the correct value for your projects.
4. Close DP.
DO NOT SAVE THE PROJECT WHEN IT ASKS.
*5. Open your soundcard's control panel.
*6. Set the sample rate to the correct value here.
* Not necessary on all devices
This fixed the issue for me. Now the affect projects quantize correctly. I only had to do this once on an affected project.
This issue appears to be related. It also was happening occasionally, and now it hasn't happened all afternoon since figuring out this 'fix'.
What caused it? I have no clue. I've used various sample rates due to necessity with no problem in the past. The issue was reproducible on other DP user's systems given just an affected project.
4 days of

later... and finally work can continue at a normal pace.