I have never tried this, but has anyone considered the following method of filling the HWH with solution?
Remove the aerator from the sink faucet closest to the HWH.
Attach a hose with funnel to it. (garden hose adapters are available)
Turn on only the hot water.
Fill the hot water tank.
Getting it to burp might require opening another faucet or pouring slowly with no sag in the hose.
My experience with such things is "don't disturb anything unnecessarily" like the pressure relief valve. You may be replacing it because it leaks after being disturbed.