Yes it is legal to pack them out, no proof of sex required. Law doesn't specify where you need to be or when you need to process the carcass. No different than bringing the carcass home and cutting it up and then taking some to a butcher for further processing. When you take it to the butcher you don't need the head or tag. Just your own identity for his book. I leave the doe head in the woods and usually just take out the skull cap of the buck, carry the completed tag in my pocket. Been doing it with every deer for MANY years.
First trip out is to drop off the weapon, heavy clothes and all hunting stuff. Change to light work clothes, carry in 2 buckets with 2 knives (skinning and caping), sharpening steel, pack meat saw, couple of plastic bags for heart and liver. Quarter it and carry out 2 buckets of clean meat.
For me has nothing to do with dragging ease as I can get my 4wd tractor anywhere on the property. It's just so fast, easy, and a clean way of doing it. An animal doesn't skin any easier than when its hot. Doesn't cool any quicker than when it is skinned immediately. It is never gutted so there is no potential to contaminate anything with a dirty knife or hands, even gut shot there is no mess, no broken bladders, no broken intestines, no rimming out the colon. No getting dirt on anything from a drag. No bringing home ticks or deer keds, only a few bones to take back out in the woods. Most natural thing for an apex predator to take what it wants and leave everything else for the rest of the ecosystem rather than turning it into refuse in a landfill. Handled much the same way as a steer coming into a slaughterhouse.
§ 2328. Shipping or transporting big game.
(a) General rule.--Unless properly tagged, it is unlawful
for any person to ship or transport the carcass of any big game.
The tag shall contain in English the name, address and license
number of the owner and the location where the big game was
(b) Portions of big game.--Any person may transport an
unmarked part of a big game carcass that has been legally taken
and cut up. Such person shall, upon request of any law
enforcement officer, furnish the name, address and license
number of the person killing the big game and any other
information required to properly establish legal possession.