At the moment I would consider a split focus to contact the Bastard and the Twins. We're running out of time to influence the course of the civil war and need to set up to do so soon. We do need to contact the Border Princes as well, but that can probably be left until the turn after next. But none of those would be exactly wasted.
The Bastard, for all that Illona isn't impressed, strikes me as potentially very interesting. Hadi sounds almost like a fantasy novel protagonist, or some mythic Persian hero. The secret son of the King who arises in the provinces to save his family from the corrupt satrap and raises a rebellion to restore the rightful order? Yeah, pretty heroic stuff. If he has the chops to actually see it through.
I really don't like the idea of stirring up this hornet nest with these sorts of candidates. Look at the first of the first False Dmitriy in Russia during the Time of Troubles; supposedly the son of a prior tsar, he gained the support of the people as well as the at-the-time powerful Polish-Lithuanian Commonwealth. He managed to sweep aside the son of the unpopular noble who had previously been the regent and had claimed the throne for himself when the Rurikid line had run out (that noble had just died, leaving the throne to his young son) and was himself installed as tsar. Relative to our situation, a lot of that seems to be nice benefits that we are presently lacking; the guy could at least claim to be the last remnant of the legitimate line, while the Bastard here is, well, a bastard, and he's seeking to displace the guy who was explicitly designated as crown prince. That leaves extremely little room for noble support without even factoring in the peasant revolt that he's leading.
Despite the advantages that False Dmitriy had going for him, what happened? He was a bit too Catholic for everyone's tastes; the people's passions were set aflame by concerned nobles who thought that he might try to essentially impose Catholicism on everyone, and his special tolerance for them appeared to confirm that. He ended up killed, cremated and with his ashes shot out of a cannon in the direction of Poland, his supporters (in particular, people suspected to be Catholics) were massacred and the whole episode would cause more trouble for Poland down the line.
Even if the guy has astonishing success, the very malleability towards our faith that would make him useful to us could be a weakness that people who wish to resist him might use to unify the people of the south against our alien faith and empire. He may feel encouraged once on the throne to denounce us and our influences to shore up relationships with internal factions... and then where would all our expended treasure and effort be?
The one thing that I most want to avoid is a protracted conflict. Every day of war is an additional day where the memory of lucrative trade that once flowed from our direction to theirs in peace becomes fainter, a day where the incumbent's troops gain yet more experience in bloodletting (the only thing that they are lacking in), and time for them to be an unstable mess that anything can arise from. I especially don't want a way for them to associate our empire with some manner of treachery and an extension of their hardship, because that'll help to harden our relations into a permanent enemy status while I would really prefer for us to be trade partners and keep our borders at the nice natural cut-off where they are now.
Also, an actually important question:what's the stance on same-sex relationships/marriages generally? Heretical, frowned upon, accepted, etc?
If I recall correctly, it's regarded negatively but not tremendously so, mainly as a decadent sort of practice. One that you can't get heirs out of, either.
EDIT: Found it!
"The passion you two have for one another is nice, but you're doing it wrong."
More seriously, homosexuality is not expressly forbidden, but if it happens it's generally not discussed openly, and you're still expected to get married and sire children. The passion of intimacy is considered sacred wherever it is found...but if it gets in the way of important things people are going to talk, and it's not going to be nice.