Need some sort of rivet to allow to cardboard discs to rotate independently

[bendover]

I'm building an educational contraption for my children out of 1.5mm cardboard. It's made of a base disc on which I want to place one of several add-on discs (with holes in them). Both kinds of discs are about 8.5" in diameter. I need those add-on discs to be easily placeable and removable onto the base disc without hurting the cardboard. I also want the add-on disc to be able to rotate independently so that the holes show different parts of the base.

For that, I've been trying (and actually bought) magnetic rivets, the kind that are used for purses and other leather applications. Here's one that I bought. However, there are two issues with these: 1. the rivets are thick, leaving more like 5mm of space in between the cardboard pieces, whereas the two need to be flush or almost flush, and 2. the magnets are too strong and detaching the two pieces would result in the cardboard taking a lot of force before the detachment happens, and in time that would ruin it. I've attached the rivets to two smaller pieces of the same cardboard to try them out. Here are a couple of pictures.

There's magnetic adhesive strips like these that seem like they could work, they are thin, they may not use very strong magnets (I don't know for sure, I'd have to try it), both of which would be plusses, except that they wouldn't allow for a good rotation of the add-on disc onto the base disc, because there's nothing preventing the add-on from sliding sideways when I push to rotate it. That would defeat the purpose.

Any ideas on what I could use? I'm fine with having to screw on the add-on disc as part of mounting it, as long as the two requirements (that the discs can be rotated independently while keeping their centers aligned, and that it's relatively easy to put them together or take them apart from each other) are met.

If there's a screw, I could see it working if I strengthen the cardboard center hole with washers. I'd strongly prefer reel-style washers (like these), but I'm open to suggestions.

I could use references to specific products that I could buy or that I could research by name.

It would be cool if there were this snap-on thing that you can press on to release the add-on disc, as sketched here. Or even better, this thing, which would allow stacking of multiple discs.

[Craft Forums]

[bendover]

I may have found what I need: Loxx fasteners.