I have to agree with Pete and Anthony with regards to Vernon's Symphony and Chris Capehart's routines. I have seen many people do the Symphony over the years (some did it justice, some just hacked away at it), and the structure of the routine is such that they always got a great response no matter the performer (not sure if that is good or bad for us?!). Luckily for me, I have been priviledged to watch Mr. Capehart in person doing his rings, and it is also a phenominal routine. If you get the chance to ever see him - go!
As for the Richard Ross routine using three rings. It does... and it also uses six. The book "Richard Ross - The Ring Routine" (1982 - Manfred Thumm, The Magic Hands) has two routines. One for three rings, and the other for six. Both are intended to be done silent to music, with a couple of touches that allow some audience interaction if the situation allows. Although my early attempts at doing the rings were with the Symphony, the silent routine I have been performing since 1982 is based on the Ross three-ring routine. I am quite happy with the results, and have been able to do it in virtually any performing situation (inside, outside, surrounded, etc.).
While you're still researching, check out the newly released "Lord and Master of the Rings" DVD by Jim Cellini. Cellini is known for being one of the best street performers ever. His ring routine is second to none (and being a street performer, you know it can be done out of doors). It is performed silently to music, only uses two rings, and there are moves in his routine that I have never seen anyone else do. The rings literally MELT through one another during MULTIPLE passes - not just in a move here and there. (I saw Jonathan Neal do his own beautiful 2 ring routine at the Castle in the early 80's with thick gold-colored rings, and I don't remember how similar the two routines may be. Mr. Biro?) The Cellini DVD is very well done, and the moves are clearly taught by Cellini. Some friends and I had the opportunity to spend some time with Cellini a couple of years back, and he did his rings for us - again and again. Pure genius.
Hope this helps.
- David Oliver