If you are looking to age the meat in Phoenix, and you do not have access to a walk in where you can hang it, then you can get by with your fridge or a cooler. I generally recommend against using a regular household fridge because often times the fridge will have had onions, garlic, ect. in it recently that will taint the flavor of the meat. If you use a cooler you want to create a rack in the bottom to keep the meat from having direct contact with the ice. If you are going to try to age the meat I would recommend doing a good bit of reading on the internet on how to age wild game before you do so.
As to why the backstrap was tough, I cannot say, but don't think it should of been. How much experience do you have cooking wild game? How did you prepare it? Whenever you are preparing any type of meat you want to make sure that before it goes into your mouth it is sliced relatively thinly across the grain and not with the grain of the meat.
Also did you check the temperature of the steaks with a meat thermometer? Often when people are accustomed to cooking beef but not wild game they overcook it and make it much tougher. The meat is a much darker red, and the red persists through the cooking process much more than the dyes they put in beef. Consequently people who aren't used to cooking elk will look at the inside and think it is still raw/rare when if you stuck it with a meat thermometer you would see it is medium well to well done.
My favorite way to cook elk or deer backstrap is to cut it into ~3/4" to 1" thick pieces across the muscle fiber. It should end up with more or less a circle as the shape. Make sure they are warmed up to room temp and salt both sides. Let this sit for ~20 minutes so that the salt denatures the proteins on the surface but doesn't go much farther. It is okay to oversalt a little because some of the salt will run off in the juices and you are also compensating for not being able salt the inside. While you are waiting for the salt to do its thing either get the grill or a cast iron skillet going. You want to get it HOT before cooking so that you sear the meat as soon as you put it on. I use a light coat of a light olive oil either on the grill rack or the pan and put the steaks in immediately. Make sure not to overcook it, if the steaks are cut on the thin side I will only do about a minute and a half to two minutes per side, and then let the steak rest for 10 minutes before eating it. While the steaks are resting I normally put some fresh ground black pepper on either side. Once again I advise checking with a calibrated meat thermometer because the meat will be much more red inside than you are accustomed to with beef.
