Vault 4 Key - Farming Tips?

As I understand it, each Cryo key is obtained from these sources:

1, 2, 6 -> Intercept, Lockdown, Convoy, Pinwheel, Upper Complex

3 -> Wraith Warden

4 -> Scorch Warden

5 -> Tox Warden

I've also heard that the Pinwheel room specifically can *very* rarely drop one of the gold keys, so I figured that farming the Pinwbeel room would be a bad way of getting Vault 4 keys, and that I'd rather try to farm the Scorch Warden. The problem with that is he rarely spawns. It seems like a 1 in 3 or maybe 1 in 4, at least in Sponsored queue, and the key isn't even guaranteed either.

So is it actually faster to repeatedly roll the dice and try to find the Scorch Warden and then hope he has a key, or does the amount of time wasted on runs where he never spawns make farming Pinwheel faster?

All I need is the subroutine and I already have a key, I just want more than one key as backup in case the first attempt is a dud.