I still don't think Elidibus had anything to do with Thordan being a primal. Elidibus had everything to do with the war and instability in Ishgard, but to me it was clear Lahabrea acted on his own. Seeing Elidibus and Lahabrea together in 2.X does not imply they were working together on personal goals. In fact, straight out, we know Elidibus doesn't always work with the others always and the others aren't happy about it (Nabriales scene in 2.1) and we know Lahabrea and Elidibus were already having a falling out by 2.55 (which probably stems back further, by Elidibus' admission to you). The absolute clencher for me is Elidibus saying at the end of 3.0 that Lahabrea was acting on his own to start a Rejoining.
Now, if Elidibus aided with the Primal pet project, what would have been the 3.0 end goal? Probably the same as Lahabrea's: Azys Lla, the Triad; Thordan being a primal is worthless unless there's something to use the primal form on, be it to drain Hydaelyn or whatever else needs draining or something else entirely. Elidibus would have been mostly happy with the way things were going, there's no reason for him not to be, everything was going perfectly. Instead we get the opposite: the epilogue statement clearly shows he was not pleased by Lahabrea's actions and did not want Thordan to awaken the Triad (by the way, I think we can chalk this one up as confirmed by the artbook: the "Triad Core" is the main feature inside the Singularity Reactor, I posted some pictures of it in the artbook thread) - and possibly does not want the Triad awakening at all (sending the WoDs after the Primals and aiding you in your EX primal killing). If he was displeased by Lahabrea bringing Thordan to Azys Lla and the Triad, for what purpose would Elidibus want Thordan to be a primal?
Hence, he probably had nothing to do with the Thordan project.
My view of that scene behind Thordan was more keeping tabs on Lahabrea, stopping him from doing something stupid, rather than working directly with him on the side project. Stupid, of course, is exactly what Lahabrea does when Elidibus leaves him be.
But, eh, we've had this debate already.