I also learned that you can add new disk features - up to a point. I put back the disk_clay, disk_gravel, and disk_sand and named my disk feature for 1.18.2 disk_concrete. All this worked just fine. When I tried to add disk_concrete_1, disk_concrete_2 to that list, 1 & 2 didn't show up. Not sure if it's due to the way I named them or if there is a limit as to how many disk features you can add to a biome.
I think you should be able to get your custom feature working just fine with the adjustments mentioned above, and if you don't want to completely replace the clay block, you could just rename your disk feature to something different so that the vanilla clay disks can be placed as well.