Congratulations on the deer!
Since you have the skin off, I wouldn't worry about getting the quarters in the fridge tonight. Especially if you have it hanging out in a shed or unheated garage and it's going to get down in the 30s. That's about the normal temperatures around here during deer season. And it always seems it's the middle of the night for us too by the time we get the deer home and skinned out. We just let them hang in the shed overnight and cut them up the next day. I've never believed in letting wild game meat "age."
There just isn't much meat on a deer's rib cage and what there is, is usually blood-shot. So we usually end up throwing both sets of ribs away after cutting as close to them as we can. We might have an advantage on you there - we live out of town so I just take the rib cage and bones way out in the back field and bury them deep enough so the coyotes don't dig them up. The hide is worth $5 to $8 at a recycle place in town, or we sometimes take it out to the Indian Reservation where they'll trade us a pair of cheap buckskin gloves for it. I've never been interested in tanning one, but some folks do. I guess if you don't have a place around that accepts deer hides, you'll just have to find a way to dispose of it.