Use riser blocks to elevate the router so that you can cut the billet slots from above. You would have to cut to full slot depth, but you can go very slow and you would be able to actually mill the slots to any width you want and take clean up cuts on the sides.
You would need two different riser blocks, one for joint and one for butt sized billets. Remove the router bracket from the cross slide and place the appropriate riser block between the cross slide and the mount. You would need longer fasteners, obviously. This would work fine if:
1. You set the router in the clamp for turning and never changed it.
2. You always used 1/8" endmills with depth rings so the endmill projection never changed.
3. The OD of your ring billet blanks when ready for slot cutting are consistent and not too oversized in order to minimize the cutting depth. Always use the largest endmill you can get away with since you would be cutting to full depth.
Set the router positioned for turning. Once you are happy with it, take some measurements. Be as precise as you can. From these calculations, come up with what you think would be the right riser thickness for joint billets. Add .100 to the thickness (so you can whittle it down later after tests). Test. Adjust block. Test. Once the riser block gets you cutting to the proper depth for joint ring billets, some simple math will tell you what thickness to make the other riser block.
Edit: I don't know what depth you could actually get away with for a 1/16" endmill. For a .900 joint ring billet, cutting .100 deep is probably doable. For a 1.3" ring billet, cutting .188 deep might be asking a whole lot.