I did something similar to what I described with my jet lathe when I got frustrated with stitched ring designs I wanted to do would not match the width of a slot cutter (vertical router position) or already owned endmill (horizontal router position). I never considered getting slot cutters custom ground to a particular thickness. That sounds good, but when stacking veneer strips to do different ring designs, after laminating them together, the thickness often varies from one set of veneers to another.
I also liked the idea of actually milling the slots in a conventional sense with finish passes taking off only .002 of stock on each side for a cleaner cut. When I was using my JET to make ring billets, I was using a 5C spin indexer mounted to a pedestal that brought the billet up to lathe center height. Instead of raising/lowering the router I made riser plates for the indexer. I raised the billet up and used a 1/16" slot cutter to mill slots from below the billet with the router in the horizontal position. This way I could use the cross slide to mill a slot to any thickness I wanted, as long as it was > 1/16".
When I read the OP's post, I was reminded of what I did. I sort of thought he was looking for more slot thickness options than 1/16", but I was mistaken and my post probably wasn't helpful. After more posts, it sounds more like he wants to be able to turn, then make a ring billet without changing the router position, router height, and even the router bit.