You need to find a rifle with 0.473 inch bolt face - get a reloading manual to get an idea about which cartridges to look for.
As far as 7mm's go,
-The 7mm Remington Magnum uses a 0.532 bolt face.
-the 7mm Mauser is 0.473
-7-08 is 0.473, no suprise there.
Other cartridges with 0.473 bolt faces -
- 280 Remington (long action),
- 284 Winchester,
- 270 Winchester (long action),
- 225 Winchester,
- 22-250 Remington,
- 243 Winchester,
- 6mm Remington (long action?),
- 250 Savage,
- 300 Savage,
and others.
Some gunsmiths open .223 Remington class (0.378) bolt faces to 0.473, and my guess is that just as many, or more, won't do it and recommend against the practice.
The ring in a ring design of the Model 700 action is a really good feature for protecting the shooter against cartridge head separation or other case failures. Don't monkey with the integrity of the design, use the right bolt dace to start. Clapped out Model 700's are available (but hard to find around here because the target shooters buy them up as soon as they hit the market) for about $250 to $300.