Nanites
Concentrating on the nanites does not seem to promote healing. Doc, checking his monitors, notes that the nanites stay concentrated in the prefrontal cortex, plus the thyroid and the adrenal glands. The nanites are also active in the immune system, but this activity seems to be focused on eliminating pathogens and other impurities. This might promote healing indirectly by combating infection, but the nanites don't seem to be stitching bone or muscle or organs back together.
When Ohanzee drinks a beer, Doc will notice the nanites going into a frenzy to scrub the alcohol out of his system. Feel free to RP all of this how you like.
Borders
Chino already rolled for border crossings, and knows several that he think will work. However, these are all remote and will present some challenging logistics. (For example, getting across the border is easy but you won't have a vehicle on one side. Great, are we just going to hike through the snow and mountains for for two days with Ohanzee levitating the obelisk the whole way?)
Katsina mentioned a quick trip into Denver to deliver a quicksilver photograph to DIMR's headquarters. She was thinking of this being a very brief trip without everyone tagging along, preferably just the people with strong SINs who could cross borders quickly and legally. Ace, Ohanzee, and Katsina would be the most logical candidates, although it's unclear whether quickened spells will catch the attention of border patrol. Then they would return and rejoin the rest of the group (and the obelisk) back in the PCC, where the meet would occur.
Or you could just hire a courier to take the the quicksilver photograph to Denver for you, but Katsina didn't think of that.
Memory tests
Blue Team is reasonably certain that they've known each other for some time. Does that mean two months (just for this job), or six months (enough time to encompass the BTL recording), or longer? That's still uncertain.
Both Doc and Ohanzee feel like there might be a clue in the various nanite levels of the team:
Doc = 10
Chino = 6
Sam/Ohanzee = 2-3
Ace = <1
Katsina = 0
This suggests that Doc is the source of the nanites. The fact that Chino is the second-most infected either implies that he and Doc were close buds and spent a lot of time together (which the BTL recording would certainly suggest) or that they've known each other longer than they've known Sam and Ohanzee.
Ace's level of infection is maybe 1/3rd of a point. Maybe you could do some math and say "Doc has known Ace for 48 hours, and this is how infected he is after 48 hours, what does that suggest for how long Doc has known Sam and Ohanzee", but there are several factors you don't know about the infection. Namely, how fast the infection spreads from person to person, the importance of physical proximity, how quickly the nanites replicate by themselves once a carrier is infected, and so on. And, of course, you don't even know if Doc has been infected with the nanites for the whole time that he's known the rest of Blue Team. Perhaps the nanite infection is relatively recent but Blue Team has known each other for ages.