Trying to find where water comes from is always a **** shoot. You stated that both sides of the coach are getting water in the bays. I guess first off did you notice water in bays before the rain came. Did you notice water before the gray tank over flowed.
Looking at pictures of your unit it looks like the slides cover the doors to the bays. I would however look at the weather striping on the bay doors. Look mainly at the top of the doors where the slides a line. The weather stripping may be folded or not in the correct place. But you said in more than one bay. If you looked after the grey tank it could be from that, however the water would have to run through the floor to get to the bays.
I used to have a Thor ACE and each outside bay was a plastic mold by its self. I got water in the bays also and it was caused by the seals not being correct. In looking at the bays I noticed an area that was made for a drain hole. I took my drill and made a few small drain holes to at least take care of the bays holding the water. I know that did not solve the problem but it did solve water in the bay.
I would go to the Winnebago Forums also and ask the question.