You might well damage them, as the drivers won't see the correct restoring force. Also if those ABRs have leaky surrounds those speakers are not going to sound correct.
With your level of experience and not getting a second chance if you ruin the ABRs, I would have them professionally restored. You seem to really be attached to those speakers for some odd reason, and if you ruin them I doubt you will ever duplicate that sound. Personally, I would not give those speakers house room, but you seem to like them.
I get why you view the speakers as inferior, they probably are, but a couple of things; I do like the sound and the open musical feel they offer, to duplicate it, we're probably looking at $600 to $1k, and a possible bunch of returns along the way, since I like this sound, why go through the potential returns hassle and spend $1k just to get me to a similar level of listening happiness.
To the assertion that I will find them impossible to duplicate, I don't think so, after listening to these FS52's, while they do crumble at loud levels, on moderate to low levels, I find them to be close to the inferior Sony Towers, thus it certainly is possible but it certainly will take some trial and error.
In essence at moderate levels, I can't discern that much difference with the old paper cones and the material that these Pioneer FS52's use, it is just that as you go louder, the sound gets muddy and boxy and closed in and the tweeters get bright, while when I raise the volume on the SS-U501 Tower's, it opens up, as if I'm in the middle of a Symphony Orchestra.
Finally, I did come across a few modern brands that do use paper cones but again, this affords me more time to test speakers at a slow pace.