I have transplanted during flower because of similar problems and everything went fine. It's not ideal to transplant during flower but you have to weigh that against the trouble the plant will have if you don't. I would transplant into a larger pot with very light airy soil. Perhaps 30% - 50% perlite which will help pull the moisture out of the sodden soil.
Take the pot with the plant, put it inside the new pot and fill soil all around it, packing just enough to keep it in place. Pull out the pot, remove the plant from it and slip it carefully into the hole. If you do that carefully you will see little or no transplant shock.
Before you do anything, I suggest you carefully slide the plant out of the container and check what's going on.