Excellent day in the lab.
I got the elevator key copied, so I’ll never get locked out of the lab. I did a successful test of the mechanical relay.
I rearranged the equipment rack to make room for the coil power supply:
Using 80/20 I constructed a 4U rack mountable chassis for the coil power supply:
Next I mounted the electrical hardware on the sheet aluminum. I started by using a transfer punch to make guides for the drilling. Then I drilled and tapped the holes for M3 bolts:
The first circuit I wired up was the 2 KΩ bleed resistor. Here you can see the bleed resistor wired to the capacitor via a switch. Turning ON the switch bleeds the capacitor:
Next I wired the DC side to the capacitor while minding polarity. Put a voltage meter across the capacitor:
Using the variac I slowly brought up the capacitor to 300V:
Once the capacitor is charged… it holds its charge without much dissipation after the variac goes off.
I was planning to power the relay using this ATX power supply (24V across +12V and -12V):
But during my initial testing it started squeeling and soon blew its fuse!
There was no short circuit that I could see, so perhaps it just died of natural causes?
Anyway… it reminds me: I should fuse the coil power supply before I go much further!
Prometheus Fusion Perfection 
The computer supply is not designed to be used as a 24V supply the way you are using it. I think you killed the supply.
Perhaps. All I did was briefly put a voltage meter across the -12V / +12V.
It blew its fuse long after I removed the voltage meter.
i read somewhere that atx power supplys are designed to be under load or will fail, perhaps it died because you had it on without load
I use old ATX supplies all the time for various projects. IMO they can take a bit of abuse. I’ve left them on with no load for extended periods without issue, but maybe I’ve just been lucky. Dust is their main enemy. I haven’t tried it but I’m pretty sure you cannot connect power between the different ‘rails’, e.g. don’t take the -12V from one connector and the +12V from the other. It needs to come off the same rail, which also limits the wattage per rail.
The other posters are correct, that you can’t use a computer power supply in this way. If you are looking just to charge the capacitors, a simple 24V DC power supply isn’t hard to make. It may be worth it to buy a used bench power supply with a variable output so it can be used for different applications.