So, it turns out I was fundamentally misunderstanding the process for processing calibration frames.
I was ready to jump into this thread and comment that Darks aren't required, and that I was only testing with Flats... Turns out, that's the whole reason it wasn't working in the first place.
For the last year, I've been using my DSLR and taking Flats and Bias frames no problem. Calibrating and Integrating my stacks worked no problem (I dropped darks due to the unreliability of taking them at the same temp as the Lights). However, when I moved to the cooled camera, I stopped taking Bias frames (since I had heard anecdotal evidence that it causes issues in some ZWO cameras). I took Darkflats with the Lights, and everything was good for a few weeks. But I didn't realize that I had to include Darks / DarkFlats as a baseline for the Flat calibration to work. I was under the impression that the Dark / DarkFlat subtraction was an optional step. How wrong I was!
Thank you so much to everyone who commented. I've been struggling with this issue for the last few weeks, wondering why my stacking was not working where it worked in the past. Thank you!!