I typically throw them into doubled-up grocery bags (they do bleed a hell of a lot when head shot, and I always head shoot them) and then into the main compartment of my day pack. All my survival gear and stuff fits in other compartments. I can get 5 or 6 of them in there, and by that point I usually stop and clean them all and then keep hunting, or drop them off at my truck and go back out. The reason I don't clean each one after it is shot is because I wear nitrile gloves when I clean them (to guard against tularemia, regardless of how low the risk is) and I don't want to go through 10 pairs of gloves on a day trip.
A few years back I was fairly easily limiting out (10) in 4-6 hours on a good day in my favourite spot, so I've carried a lot of hares. While the above method worked well for me, it sounds like Hoyt's got a really good solution, too. There were a few times that the return trip to the truck involved 5 or 6 km on snowshoes with 6 in the pack and 2 in each hand. With the rifle and the rest of my stuff, it was a good workout.
By the way, the best recipe for hare is, hands down, Hank Shaw's Sardinian Hare Stew. ht tps://honest-food.net/hare-stew-hard-times/ I first tried that recipe about 4 years ago and I was shocked at how delicious it is. Then a couple years later I was watching Meat Eater and Steve was out hunting with Hank. Hank blasted a Jack and later in the episode he cooked up the Sardinian Hare Stew for Steve and himself. Steve said it was the best thing he had tasted in a long time. I wasn't surprised at Steve's reaction at all. Make sure to find some quality saffron for that recipe. It is a key ingredient. On another Meat Eater special, Steve reminisces about that day that Hank Shaw made a gourmet meal out of a critter that most people would hit with their car and not even think twice about.