For sharps and other iffy stuff, buy online. Deliver to your destination. Mail home Parcel Post. More expensive, but no TSA hassle.
Carrying on Medivac flights should be no problem, if you are acting in your medical capacity. Carry your credentials and orders, employment contract, or whatever. The local carriers, if really small and local bush pilots, should be cool with your kit. But keep all the iffy stuff bundled together in case they need to load it separately in the cockpit or something. Fuels and other flamey stuff is likely to more of a problem than pointy stuff.
IIRC, you are military-associated. Can you beg or borrow the "military sleep system" from any of your connections? It has an inner and outer bag, as well as a Gore-Tex bivy. It will keep you plenty warm and dry.
You are welcome to borrow my Gore-Tex bivy for the month, if you need it, for shipping costs.
I've been extremely pleased with my Fenix AA flashlights. Bring all the batteries you can.
Don't forget to bring some small thank you gifts.
Do you want a medic with 30 years experience, including austere medicine, to tag along?
Jeff