If you are using it as an interlock relay,why do you have an operate time delay?
Is it also being used for the slow start function you asked about before,or is it just that you need the electro to make the DC relay work on the halfwave rectified pulsating DC?
If it is supposed to cut off the HT to a valve Amplifier,you could drive it off a bridge rectifier from the filaments instead of your current setup,& filter the supply properly.
The interlock switch could then just break a clean DC feed to your relay,& you could ditch the Electrolytic.
If you need the operate delay,you may be able to put a diode in line with the electro,where it can charge to give the delay,but not discharge through the relay coil,so the relay will drop straight out.
As the cap will have to discharge eventually,you will need to have a higher value resistor across the coil all the time.
I'm not sure this will work with the pulsating nature of the halfwave rectified AC.