I have a hold of it...with my hand...
Sorry, I'm in a happy mood.
The bar and emery are long enough and the bar has no handle so I can grip the butt end.
A little different to what you have designed but serves the same purpose as long as the bar is perfect in size.
I like your idea of Toothpaste, it might work and the idea being that it is not going to remove any great deal of material if only the finish inside rings but give you and idea of any high / low points. Valve Grinding Paste also maybe but the very fine one. Been 30-40 years since I ground valves.
Anything that is very, very fine abrasive wise.
I can't remember the grade of emery that I used with the BRT gear but it was super fine grade.
Now, Aluminium Rings are way softer than Steel so apply to suit. From memory my Kelbly Aluminium Rings took one turn, the Ken Farrel Steel Rings a few turns and a short pull. These are top end CNC Machined Rings worth a few hundred bucks but also near perfect so one little light touch. Some other cheap rubbish might take a bit of work but don't go too far and reduce the diameter inside.
Then after all that I use a Tension Wrench on all my Rings and Bases.