One source is Rio Grande. 1-800-545-6566 or riogrande.com. They are jewelry suppliers for jewelry makers They have display items and ring tray inserts and slotted ring boxes. I've used them successfully over the years. I have no idea if there are minimum orders nowadays, so ask.
Also check out Store Supply Warehouse and look up slotted ring organizer or tray. You will get some additional information.
I cut 1/8" hardboard about 1/16" undersized overall. Then cut, wrap, and hot glue fabric store felt to the hardboard. All the glueing is done on the underside. For bottom lining, I add a piece of thin quilt batting under the felt. By cutting the hardboard pretty close, it's a nice sliding fit and easily stays in place.
That is nice work. I am looking for some cardboard for the bottoms. I looked at scraps of Laminate like Formica, but it does not seem to lay flat. I have 1/8" plywood and may use that.
I am scheming on secret compartments but have not worked it out.
I went to Michaels for dark blue velvet, but all they had was black. I will try Jo-Anns today. And I will see if they have card board. Michaels did not.
I will also try to find foam tubes. How about Backer rod from the weatherstripping department?
The video below describes how padded interiors are installed in gift boxes. I found this when looking for examples of french fitting such that that found in the boxes that hold older drafting tools.