The preferred method would be to remove the existing flange, extend the pipe and install a new flange, but often that can be a cost prohibitive method.

The rings you are describing are properly called "build-up Flanges" and they are the code compliant proper way to extend the flange when resetting the flange cannot be economically achieved.

I've used one here and there, but more than one at a time is interesting. Probably would work with the silicone - be sure to scrape the flange top really well first. (I confess that I've sandwiched some extra wax instead.

Not if this is an option for you, but there are flange assemblies that slide into the existing drain. They seal the gap with rubber rings/gaskets between the two pipes. I got one at HD and used it insert into a lead water closet elbow - worked perfectly.