I am aware of a few people on the internet that use a Nelson Long Flap or a Camper Long Flap for credit card touring, where they bring no camping gear, they are sleeping indoors and eating in restaurants.
I am aware of one person that has used a Camper Long Flap and an extremely light weight tent and sleeping bag, he was primarily credit card touring but occasionally camped when he was unable to rent a room for the night.
I bought a Camper a few years ago to have for credit card touring, but have not used it.
I used my Nelson Long Flap on one tour, it was supported by my Ortlieb Back Rollers underneath it. Photos attached. I mostly used it for food on this tour. It worked well because I could easily vary the amount of food in it. To give it more structure to hold its shape, I put a piece of cardboard inside the Carradice bag. The cardboard worked well enough that I later replaced it with a piece of Coroplast which essentially is a plastic based corrugated cardboard.
But, I have generally chosen to use a dry bag instead of the Carradice bag since that trip, the time to thread the leather straps through the saddle were much more time consuming than other options that now use. On my touring bikes I use a Brooks Conquest (or on one bike a Brooks Pro). These saddles lack saddle loops, but the conquest has springs and I can attach the Carradice bag straps to the saddle spring loops.
For several years I have used a Pendle on one of my bikes for day to day use. I also have a piece of Coroplast in that, last attached photo, the Coroplast is white. The Coroplast is not attached to the bag, it just sits in it loose. The bag has a much better shape when not full with this to give it more structure.
If you try something like this as a stiffener, I would suggest first trying paper based cardboard from a box you plan to discard to see if you are happy with it first.