You could modify the design to be a pressure fit with no ring around the button. If I had the ability to make them I would, because you have an audience that needs something that will hold their round
mods up when laid down. Better yet, just design a table top cradle that can be cast inexpensively for
mods of varying sizes. You could do a dual or even a triple reduction of the inner size of the cradle that would fit mods of 1/2, 3/4/ and 1inch diameter with a simple step down in each size from the inside holding area of the cradle. I don't know if those sizes are what you would need of course, just an outline of the design.