Concentrate on just finishing the main story quests, not necessarily CLEARING those mines. Try clearing the last 3 repeatable mines as many times as possible to collect & convert the granite to coins. Thereby getting the needed keys.
I think I had all keys collected in my Egypt Diggy within 2 days, including total clearing of the locations. I think you can do it☺
If nothing else, dig your way to the goodie boxes and chests. The materials are great. Plus, even if you only collect a couple hundred of the coins, you can still get some equipment...