Not sure if this will help with reducing ring tension, but it might cause an idea to take shape.
I have had to repair a lot of old tractor and yard equipment pieces parts over the last 5 or so years. A good friend bought a Briggs service center and will fix just about anything. As a result, I get to try and fix or make parts that aren't available any longer. On the occasion that I have to weld up a shaft or temper a piece of material and want to let it cool very slowly I figured out a system that works and most folks have what they need to do it. Of course, things can be scaled up or down to fit the job.
-turkey deep fryer burner
-large cooking vessel or similar container that can handle heat. (I've used 4" black pipe for shafts and an old dutch oven for small parts, heavy walled is better)
-another vessel that holds around 1/2 to 3/4 of the above container
-bag of playground sand
-high temp thermometer
If I know what the Before doing the welding/heating, I fill the first container 1/3-1/2 full with sand and then the remainder goes in the second container and they go on the burner. There are tempering charts as well as heat by color charts all over the net. Use one to determine your required temp. Wait for the sand to come up to temp.
Weld/heat the material as required. Then, being sure to keep plenty of sand around it on all sides, bury it in the hot sand. Again, be sure to keep it well insulated with sand on all sides. Put the lid on and walk away.
I have welded shafts that I couldn't touch with a file after welding, cut like leaded steel after drawing them with this method.