dhanson64 has pretty much described the critical factors in an acoustic suspension design.
The woofer surround is very critical to the overall speaker sound since the woofer cone is also contributing to the midrange and the upper end response must integrate well with the lower end response of the tweeter or there will, in fact, be holes in the midrange which really doesn't happen with any early Advent with the grille on if it is in factory condition. The early developers of acoustice suspension speakers, including Henry kloss, experimented with many materials and configurations to obtain the ideal solution to proper woofer performance in these systems.
I am convinced that complaints about response abnormalities with Advents is due to some one thing or another not being correct.
The woofer surrounds MUST be of the extremely compliant (floppy) variety with a 17-18mm roll. Not installed, the surround shouldn't really be able to support itself but should droop. After installation, the woofer cone, out of cabinet, should easily be able to be pushed in with only the spider offering any resistance at all. If there is any real effort, at all, required to push the cone in, the surround is too stiff and will affect the speaker response. An acoustic suspension speaker relies on the trapped air in the cabinet to control cone position restoration and NOT the mechanical structures of the low frequency driver.
I want to add a note about woofer bottoming too. That is almost always caused by insufficient airtightness in the cabinet and that is what allows the woofer cone to be able to move too freely, not the surround material. If the air seal is good, the trapped air in the cabinet will control the woofer cone excursion. The test, of course as mentioned, is to push in on the cone after it is installed in the cabinet. There should be considerable resistance to your doing so and when you release the cone, it should NOT immediately move back to its neutral position. There should be a definite delay as the air in the cabinet slowly replenishes and the cone is slowly pushed out.
Doug