The real problem as I have re-thought it is that the center panel being a bigger piece will absorb more moisture and therefore expand at a greater rate. If the door manufacture had taken that into account there could have been more clearance left for the center panel. If the center panel had been plywood instead of solid you may have escaped the issue.
A mild winter usually means more humidity in the air. I wonder if your cover may be promoting higher humidity within the TT? Do you have any vents or anything left open? May have been better off with them shut.