Hm.
If one were to engage in an Elias Crichell-esque level of Clan Rules Lawyering, You could make an argument that a Trial of Annihilation is also a defacto Trial of Possession for the annihilated clan's assets. So, Territory and Material taken by the annihilators would then be fair game for you to trial for.
Now, were it a proper ToA, you would likely face repercussions in council for dropping in and interrupting the ToA by ToPosession-ing those newly claimed assets. But since we are not talking about a real clan doing the Annihilating, no one is going to complain on behalf of the spheroids. And the Jaguars might rankle at you taking some of their territory and former possessions, but if they had the strength to DO anything about it, they would not have been in those dire straits to begin with.
Basically, you could do what the wolves do ninety years later on Tharkad. To thwart the Falcons, they show up and declares their own trial for half the planet. They're not exactly doing it to help the lyrans, they're not friendly with them in the process, but they see the opportunity to tweak their beak, and thwart their plan to take Tharkad. Then, in this case, they just walk out on the holdings they won there.
The spirits could do the same without agreeing to anything in particular or directly allying with the Jaguars, just treating it as a target of opportunity. Drop in on Task Force Serpent, wrest control of territory and assets from them (and if the Jaguars happen to start fighting them at the same time, well, sucks to be a spheroid) and then keep what they take. It's not like the Jaguars are going to have the strength or political credibility to demand it back.
and, as you just added, I do think there is something to be said for "the enemy of my enemy"