Thanks for that. We must capitulate that any cabinet/speaker design must eventually go through "real world" final testing. Testing for oscillations in the shop is really basic and I think a good starting point with the sweep mentioned previously. If found, the very narrow frequency range may be focused on by keeping it static, then locating the source of the problem.White noise is all highs, will not excite bass much.
Pink noise is reasonable except the sub-50Hz energy may be too exciting, and the >2kHz energy adds to the spec without really stressing the speaker much.
40+ years ago EV proposed a filtered noise, pinkish with the extremes cut; the sweet trick is that the implementation could be simpler than a proper pink filter. I think it was the basis of an IEC standard.
Random noise never has the thump-thump-thump-thump abuse of real music. Put Inagaddadavida and LA Woman on auto-repeat all night long.
A pure "driver" that has no cone could be used to reduce vibration in the cabinet but add cost, complexity and draw power.