Update – thanks “floyd” for the link to another forum site that lead me to this tool.
I tried the “C-clamp” method and it did not work…those rivets are much harder to crush than I thought they would be. However, not wanting to compromise on the OE quality of the installation of my ashtray insert, I “bit the bullet” and purchased the Hanson HS-42E rivet squeezing tool ($145.00) directly from Hanson (pic below). This tool has a 4” reach and a 2 inch gap. Along with the rivet squeezer you will need to purchase a “head” and “tubular roll” squeezing die. The items I purchased were #CA2004-9, 3/8” head die and #CA2005-13, 7/8” “roll” die ($16.00 ea). The tool is of very high quality and works perfectly for achieving an OE look on the ashtray insert installation. A note here on use of the tool, the “ram” on the tool is adjustable so that you can customize it for the rivet and die you are using. There were no operating instructions provided with my tool. It took a little thinking and studying the tool until I realized, twisting the “ram” counter-clockwise lengthened the ram and clock-wise shortened it. With these dies to have the proper squeeze”, you will have to have the ram extend ¾” (with the handle fully down). Because of the 2” heat shield on top of the ashtray, you will not be able to insert the tool into the ashtray insert with both dies installed on the tool. It takes a little “jiggling” around but the process I used was to not install the 7/8” die until I inserted the front part of the tool in the ashtray and moved the back part of the tool into position (head of rivet). Then I reached into the ashtray and inserted the 7/8” “roll die” into the front of the tool, then extended the “ram” to just make contact with the rivet head to hold it in place, made sure my “roll die” was seated in the rivet and squeezed. The results were exactly what I was looking for.

I am finished with the tool and plan to eventually sell it and the dies at a little discount on ebay to others wanting it for the same purpose. I figure the discount then will be the ultimate cost of getting insert installed correctly. Then whoever buys the tool can use it and pass it on at a slight discount to someone else and on it goes…