This turned out to be a bit verbose. I guess I'm excited. I'll do my best to organize it in sections.
XP System Discussion: In my experience with running The Strange, the system for spending XP for temporary effects dosen't get much use at lower tiers. It's very painful to delay the transition from 1 Edge to 2, or to gain that second level of effort, to say nothing of the fact that characters tactical options are pretty limited until they start adding more type and focus abilities (Given that Onslaught is almost a no-brainer, our nanos are going to have very similar combat moves until Tier 2). Around tier 3 or so, the transition between 3 Edge and 4 carries a lot less weight, and gaining a temporary effect or declaring a setting detail becomes a lot more tempting. I think this slant towards higher tiers is at least partially by design, as one quirk of the cypher system is that it takes the same amount of XP to go from tier 5 to tier 6 and it does to go from tier 1 to tier 2. I believe that it's expected that early on players will focus primarily on advancement and progress fairly quickly, while players with more developed characters facing greater threats will be more prone to spend XP on temporary benefits and as a result character advancement slows down as they approach the higher tiers. Of course, this is only based on my own experience, and our own mileage could vary considerably.
As such I don't think the XP will make a huge difference early on unless we all make a conscious decision to evolve our characters slowly, which may be suboptimal because it will delay the acquisition of more interesting tactical options. So it may be a bunch of extra paperwork for little benefit.
That said, I love GM intrusions. I'm a big fan of the FATE rpg system, and both the receiving and spending of XP borrows heavily from the idea of Fate points. In the Cypher system the spending part is somewhat hobbled by directly working against character advancement but the receiving part still shines. I think GM intrusions are particularly well to a PbP format, as the hardest part about them is coming up with good ones on the fly. It might end up being awkward though, I'm not familiar enough with the format to know for sure.
We could do a trial run and use the XP system as written in the rules with a time set in the future to decide wether we find it's bee worth it or not..
Player connection suggestions: Antar Es. Agia's focus suggests that she form a connection where another character gets the +1 armour advantage from her ice armour ability if they are standing next to her when she activates it. Picking largely at random, I propose that this connection be with Antar Es. It may be a quirk of his implants, or possibly a hint at a shared lineage between the numenera device that transformed him into a cyborg and whatever forces resulted in Agia receiving ice powers as an infant (she believes they came from her sky god, but it wouldn't be the first religion to be founded on a misunderstanding or outright lie). I also think it would provide an interesting trade off because Antar is much more likely to be in the thick of things than Agia, so the synergy encourages her to dive into battle alongside the glaive rather than hang back and sling esoteries. I defer to the GM on whether or not the extra armor on an already heavily armoured character might be too much. The first time it occurs will almost certainly be by accident
Player connection suggestions: Dreithik. I'm going beyond just the suggested connections since one connection seems insufficient in a party of five, I propose that Agia sees the more knowledgeable Dreithik as something of a stand-in for the clan elders she left behind (who she loved as teachers and caregivers but detested as authority figures). Therefore, Agia desires Dreithik's approval as a mentor. It's up to you, Ryan, but Drithik might in turn be interested in studying Agia's endothermic physiology. After all, a metabolism capable of operating at sub-zero temperatures would be a considerable boon for the reanimation process. Agia is likely to balk at giving samples, however.