what if we use the lasso of truth to learn about zod and then find his deal with brainiac in the brainiac archives and use it to convince supergirl to become our double agent
We can certainly take actions related to brainiacs archives, but there is no guarantee we have the specific database the brainiac/zod deal was stored on. Winning immediate salvage plan picked computers once, metropolis three times, and a single intact ship fished from the pacific ocean.
Along similar lines we also have that strange sphere we recovered from Brainiac's ship which I'm 99% sure is one of his memory orbs, detailing pretty much the entire history of their respective planet,
Assuming that the one we have is the Krypton orb and not some other random planet we could almost certainly learn about the truth of Brainiac and Zod's deal from that and tempt Kara in with access to the single largest repository of her people's history.
We can see about getting a team together next turn.
To be fair while a good team would be preferable we don't strictly need one. In the worst case scenario where we can't spare anyone else Fixit is guaranteed to make decent progress on the LMD's just by himself and we could have the twins build a dedicated robotics lab to lower the DC for the future.
Which may be the best course of action because Fixit doesn't exactly have the best coop scores with our other scientists.
The thing about the mind switch device is that the government knows about it. Eiling and Diana know about it.
Even if we could convince the shadier people like Eiling to let us use it to mind switch Supergirl with what he'd view as an unreliable civilian as opposed to a trustworthy pawn of his own, it would ruin Diana's trust in Lex if she found out, and it would provide Eiling with blackmail on Lex.
We'd be better off just summoning up a demon to resolve the situation or using the Life Model Decoy and Fixit's trait.
Additionally, even if we could convince Eiling, Diana and the government in general to go along with uploading Marie into Kara's body it will leaves us with a mess we have to clean up.
Even ignoring Marie having to get used to her new powers we'd need to deal with Kara in Marie's body, people potentially asking where Marie went, Clark being suspicious about his cousins sudden change in behaviour and people being curious why Supergirl is suddenly doing PR for LexCorp.
Outside of learning none of the stats swap or stay, they shift. Learning remains consistent for the most part (it can sometimes shift). All other stats don't perfectly align with either of the swapped characters.
To use the Marie-Supergirl swap for example, Marie would gain all of Supergirl's physical capabilities but lose any gains to martial that Supergirl gets from having practice using powers on earth or having tactical insight from being trained to be a soldier on Kandor, meaning she'd have a lower martial than Supergirl but a much higher martial than Marie naturally does. Her diplomacy would shift because while Marie would be happier with a body that resembles a blond teenage girl, she would also struggle with the fact that she's in Supergirl's body and thus has a different reputation and needs to be careful when getting angry or annoyed in ways she didn't before. Her stewardship likely would trend downwards a bit as she'd be a lot more distractable with all the new senses that would mess with her ability to focus. Her intrigue meanwhile would probably raise a bit because Marie would retain most of her ability to lie but suddenly be way better at finding secrets so she'd end up with a higher stat than she normally has or Supergirl has.
The numbers don't remain consistent with the stats on either body.
Edit: After Learning, Stewardship is the next most stable stat with mindswaps but Intrigue, Martial and Diplomacy all tend to shift unless you swap really similar people.
A related question if you don't mind
@King crimson, robotic conversion is stated to give hero units that undergo it a set bonus but can they get additional bonuses on top of that?
For example, if we have Marie undergo robotic conversion and invest all of the points she gets from that into Diplomacy to boost her to 43 could she gain an additional boost as a result of her, say, becoming less acerbic and confrontational or is there a hard limit on that?