If you are still old fashioned enough to get paper checks, each checkbook seems to come fastened to a folder with semi-flexible clear silcone caulk type stuff. This stuff will stretch like a rubber band, and stays a bit sticky even after you peel it off.
If you put some inside the band as you side it in place, I think it would not mar or stain your wood, has some thickness that will compress and has some stickiness so that it won't fall out.
If it is an original, leave it alone...put a small shim on it. black plastic electrical tape works well..
If it is repro, you can file /grind a little off between the mating surfaces, take the screw out and you'll be able to do it.
A spring type would be different. you can put a little epoxy, colored if you have some paint colors. around the mating edge with the stock.
Put car wax on the metal, and then put it on so the spring holds tight. this will make up for some shrinkage from age. the car wax, or any wax that dries to a white powder and had to be wiped off works. The epoxy will not stick to it. good for any bedding problem.
good thing is, you have not touched the wood of the gun..it can always be removed
sometimes the spring that holds the band won't come up enough. do the epoxy thing in the pin hole. , let it dry in the UP position then it will have more strength. . Ken
A slip of paper between the band and the wood should do the trick. I would advise against using silicone or rubber as they will eventually go brittle. The leather shim... I’ve not tried that. I would think that might bind the ramrod.
I think this advice of using electrical tape as a shim is a winner. Electrical tape has a slick surface, and if you stick it to the inside of the metal band, it would act as a shim, would stay stuck in place, and the slick surface would be against the wood, and should allow the band to slide in place without harm to the wood. You can stick a short price to both left and right sides of the band, and so not interfere with the ramrod.
This is just one sentence of a detailed response from Ken, and I detect a lot of wisdom in this one sentence.