I'll do my best to answer your questions. However keep in mind that there are always variables involved so that's where the common sense comes in.

Question: I live in Central/Southern WI and during bow season we often have temps in 70s to 80s during the day. The closest proccessor is 40 mins away and you are out of luck if you shoot a deer in the afternoon since they close at 5pm.

I have a extra 20 cu ft refigerator /top freezer in the garage that I plan on plugging in so it will be cold during the season just in case I need it however it is not big enough to stuff a whole deer in it unless it where quartered.

If a person were to shoot a deer and have it recovered, field dressed, and the inside rinsed with cool 50 degree water within 1 1/2 hrs what would be the next best course of action?

-Immediatly skin, quarter, remove loins, tenderloins and neck meat and place in refrigerator
or pack the deer cavity with ice to bring the temp down and then skin & quarter? Assuming that you have a cool place to hang it, out of the sun (garage, basement, etc.) I would hang it head down and pack it with ice bags overnight. This will give it a chance to "cool" down which will make the boning process easier. The trade off is that it's easier to skin while still warm.

-What is the maxumuim time a person has to skin and quarter the deer and get it refrigerated at this point? 2 hrs? This depends on how cool the area is where you're hanging it and if you pack it with ice.

Would it be better to refrigerate or freeze the quarters until final deboning and cutting occurs 24 hours later? If you're cutting it within twenty four hours there is no need to freeze it.

Would it be best to wrap the quarters in wax paper or plastic to keep it from drying out until the the quarters are ready to be deboned and final cutting takes place? If the quarters are cooled down before wrapping then plastic bags will work. If the quarters are warm then you need to refrigerate them before wrapping as they will form condensation and may spoil if wrapped or bagged while warm.

Beside common sense that that bacteria will rapidly form at temps above 40 degrees, does the FDA or USDA have charts showing how long meat will last at given temps immediatly after the kill? (i.e at 50 degrees you have 4 hours to get it in a enviroment of 40 degress or less before it forms too much bacteria; at 60 degrees you have 3 hrs from time of kill ect. ) I am not aware of any charts on the subject.

 You may want to consider investing in a chest freezer (I see used ones as low as $50), then you can put the whole field dressed deer in it and thaw and cut it at your convenience. We've done deer that were frozen for 2-3 months this way, and they where in great shape when thawed, skinned, and cut.