Well Ollie, this is another fine mess you've gotten me into!
After my wife saw your paper towel dispenser, she asked me if I could build another organizer for our pantry door and incorporate paper towel storage.
To check the space available for the modification, she got in the pantry with her tape measure and I closed the door. "Seven inches of clearance"
She played around with the paper towel roll and we agreed on a plan. Of course, this plan is subject to change at any time. Our pantry is small and about as organized as it can get. So, I will build a new organizer to fit the door. It will be the same length, a few inches wider (20) with deeper shelves for more storage.
The contents will remain basically the same, just better organized, and have room for two or maybe three rolls of paper towels. The extra inventory is stored out in the garage.
So, that is the plan. I have some 1/2 inch Baltic Birch so...