Hi Jesse,
Just some thoughts....
Typically, a filter wheel is in close proximity to the camera sensor, so that those dust donuts are usually small in size and are the ones you're trying to accommodate for with flat fielding. Typically, the camera and filter wheel rotates together. If that's true for you, then the donuts should not move with respect to the image as the rotation angle changes. Maybe there are second-order effects cause by imprecise optical axis alignment combined with flexure.
The other serious problem is, as Bob mentioned, vignetting. In that case, the camera and filter wheel will likely be rotating with respect to the various "stops" that cause vignetting, which would then be difficult to flat-field away.
I have a Meade Classic, which I bought long ago without a wedge but with a derotator. The derotator worked fine, but I only used it for a year or so. It was cumbersome anyway and difficult to use for those high-elevation images near zenith. I subsequently build a wedge and remounted the Meade on it.