Loosely,
The C&TS schedule is near 150 days from Memorial day, to the middle of October. At this rate if you had an engine steamed up every day each season, it would last about 10 years before needing a 1472 (147 days per year would be exactly 10 years). For a typical season, you would be "safe" having 4 engines ready for service. Two for daily use, one for a helper and one for backup. The FRA limits are 1472 days or 15 years (correct?). This means you will use 4 engines time in 10 years. Simple math would back your theory that two more serviceable engines would complete the 15 year gap. Any more and you start running out of time before you use up the days.
This in a nutshell does not completely take into account special trips such as charter trains, moon light or dinner trains, the various geology and other trains engineer and fireman school etc. It also doesn't account for any other off season operations like the Polar Express, which is a big draw in steam railroading.
I agree with your 6 engine theory, and raise you one more. If you factor in pre and post season maintenance on track work, Polar Express runs, and anything else that might come up. A seventh engine could be feasible. This would also pretty much mean only 4 engines could be kept hot at any one time. Because of the time, stress, and other requirements of an engine being steamed up, when one goes down for maintenance, it would stay down until it is next in the rotation.
Thoughts of a back seat driver....
Casey