That tool will get you there with the least fuss.
I do it wit just a sapping block and a ring mandrel, and a rawhide mallet.
The thing is, your desighn will stretch on the outside and compress on the inside, so distortion will be considerable. When I do seemlessly rings like this i distort my design so that when the forming is done the design is as it should be.
beautiful. i'll guess it will turn out ok. i have seen a couple rings made of coins. there was very little damage to the original surfaces. not sure how they are done, but it's pretty cool what the ring people do.