FDA doesn't allow domestic animals and wild game to be stored and processed together, so a butcher or beef processor with cold storage space will most likely turn you away.
If you take your game into Cinnamon Creek Ranch and have them process it for you, they allow you to make the call on how long to hang it. But they are not cheap.
www.cinnamoncreekranch.comMy brother does his own processing and solved for this by buying a free standing drink cooler from a convenience store that went out of business. Ripped out the shelving, installed a bar in the top, and it holds 4 elk quarters at 42 degrees neatly hung side by side until they are aged to his liking. After hunting season he unplugs it and shoves it back into a corner of his shop.