Boosting Odds of a Certain Key

So I'm currently working on the >!sanctum keys!<, but I'm having trouble with one particular one, that being the one you get from the >!vault!<

>!From the clues, it was easy to deduce the sanctum key was in the vault. the issue is that to get it, I need the correct safety deposit key which isn't consistently available. I've probably run into it on a run, but never with the vault unlocked as well. Now I'm getting the vault more often (even axed the cost so I can't be locked out of it due to gems) but now I'm having trouble finding the key. So is there any way to boost the chances of finding the key or am I at the mercy of RNG? My first thought would be picking root cellar for the outer room and getting one of the shovel upgrades, but I'm not sure which, if either, of the shovel upgrades increases my chances of safety deposit box keys.!<