Steve, in response to your questions:
For handlebars, agree 100% that Drop Bars are the way to go for a ride like this.
Gearing: my gearing is always exceptionally low. My Roadeo with 22-34-44 and a 13-30 may have been the lowest gearing out of all the riders. I need those low gears - - with the assembled orthopedic and other medical issues, and being over 200 pounds, I just really need super low gears. Patellar tendinitis means I never climb out of the saddle at all, so I I just spin up the hills. Which, of course, is a lot easier in the long run.
Most of the other riders did not have gears that low. If you're fit and not too heavy, I would say that a compact double with a 34 tooth inner would be ok, as long as you have a 34 tooth low gear on your cassette.
Two years ago, I did the ride on a Della Santa with an ultra-compact double - - 26-40 chainrings, with a SRAM 11-36 cassette.
The hills were long, but usually not steeper than 6%. Cycle Greater Yellowstone will post the ride profiles several months before the event (I think they use Map My Ride, with elevation profiles), so we can all know what we're in for.
I did the ride on a Roadeo, and I have a Rambouillet as well. IMHO both bikes are well-suited for the course - your Rambouillet (with triple) would be a great choice if you are willing to put on drop bars.
Good luck, hope to see you next year.
Max