Is a subwoofers RMS/peak wattage rating subject to the enclosure type?
Wrt excursion you'll find that any enclosure will affect this at a given input level. The closed enclosure will provide damping of the excursion all way down, while the ported version will provide little or no damping below the resonance frequency of the port. 

I would suggest to do a frequency sweep with the driver mounted in the actual box to be used, starting at reduced input level. You should test for power as you have suggested, but also for excursion. 

You will need a way to determine when Xmax is reached, and one way to do it is to use light weight pin. The pin should have a rounded head and be fixed loosely in e.g. expanded polystyrene or the like. You need to jerk the pin in and out some times to get it loose enough. The idea is that the pin is fixed at a distance from the dust cap, and when the desired excursion is reached, the pin will be displaced. Remember that polystyrene will easily move with the displaced air, so it should be a little as possible and held in position by a device made of high density material.



If you do this together with measuring the power, you will get the info you need for safe operation.