Sorry, probably mixed things up a bit, accidentally.
First you machine over-size to the required "spring" plus a couple of thou. Then compress in a bore that is the size for the correct amount of ring compression (actually they called it "spring tension" at H & G from what I remember?) and hold clamped axially (at the correct ring-gap) and machine to the BORE size while compressed. (That "couple of thou"). This means the COMPRESSED ring in the bore has a "perfect circle" and correct cylinder wall pressure. Perhaps this is just impossible for the rings as small as you are making? The smallest production process I saw was about 2" diameter. - But I was a visitor, not working there, so may be wrong with the process I remember? Also, I have no hard data of sizes etc. - which were their "secret" to get the required finished parameters and sizes.
I don't know the Trimble method. Is this a way of machining to size, then softening, expanding and hardening to give some ring to cylinder wall pressure? - This sounds like a heat treatment that could possibly distort the shape of the ring from the "perfect circle" that was the target at H & G. But they were dealing in cast iron rings that would not be heat treated. They did make steel wire rings as well, that were heat treated - but this was a time for soaking them in burning Ammonia gas at a very dull red heat to nitride the surface. Actually the steel ring shape came off a clever winder that gave the ring "tension" that was uniform when in the bore. Which meant it wasn't a perfect circle unloaded, as the end effect of the element of the ring close to an end was to give a different wall pressure when compared to a "middle" element that is supported by elements either side with the same wall pressure. There must be a mathematical paper on this somewhere, that is better than my imperfect memory from 35 years ago.
Sorry about confusion.
K