I'm not a big fan of the Field Work track - especially if you're only going to get 3 more upgrades, max - so if I was already Level 5 I'd ignore that one.
Ingenuity in the Science track is decent, but I don't like that it requires a Grit and that you can still fail the roll, wasting the Grit.
Personally, I would get Triage (+1 Max Grit with a chance to recover a Grit every time you heal someone) for sure, and either Treatment (my preference, it guarantees at least 60 XP whenever you heal someone) or Ingenuity (hopefully Triage can replace any Grit lost from failed Ingenuity rolls) for your second upgrade.
You make some excellent points.
The main draw of the field work track for me is the strength bonus (strength 2 is rough)
I guess the main choice then is if ingenuity or dispassionate is a better choice.