I have been pondering this conundrum. Nothing like a conundrum to loosen the mental sluices.......
I feel the only viable solution here, and one with extraordinary Faraday cage advantages, would be to float each toroid in a small but contoured bath of mercury.

This notion is based on Lighthouse Technology of 70 years ago, which used the same liquid element to suspend the lighting platform (but which enjoyed somewhat better ventilation!). Hydrargyum has density 13.6, and should float even a 2.1 Kg toroid down to about half depth. Of course, ca va sans dire, the toroids may need special sealing to prevent Hg ingress, but this is mere detail......
The toroids should be secured with stronger than steel, fine guy ropes from the sides, at intervals of 45 degrees. These guys should be comprised of spider web, for which purpose the Huntsman should be pressed into service, their webs having the highest Youngs Modulus. Together with the very high density of mercury, such an approach would kill all oscillation in its tracks (and unless the progenitors are removed after the construction phase, quite possibly the listeners as well........

).
A small container should be contructed of mu-metal to suitably enclose the assembly, which ideally should take on the shape of a tiny nuclear reactor (...and doubtless be just as dangerous! Ed.). It should be round of course, which may require some recuring of the mu-metal to preserve its magnetic integrity. The chamber should be sealed hermetically to prevent the low vapour pressure of Hg from affecting the health of any audiophiles in attendance; this stuff does cross the blood brain barrier after all.
Speaker cables comprising mercury in special plastic tubes have been made here in Melbourne. My understanding is that the creator died young of a particularly rare cancer, however. Various sonic reports of 'gravitas', and 'body', and 'shimmering highs' have done the rounds. An article on this very issue was published with some fanfare by Electronics Australia about 15 years ago, proposing ground ceramic fittings to contain the mercury. Sadly, no kitset was ever released. There were some rumours that the mercury needed constant replacement to deliver its best; I have no way of checking on this.
Certainly there are always options, in no way limited by the bounds of human imagination or rationality.......

Let the games begin!!!
Cheers,
Hugh