Hum. I personally have not had good results from EL84 tubes, but not in the way you describe. The volume was perfectly normal, the sound just wasn't very good compared to other options. What you describe sounds like bad tubes to me, or tubes that are not actually EL84s. And there is no trick to using them, if your Sovteks work OK then it is hard to imagine the problem is you or the amp.
What "tube checker" are you using? And is it possible it is out of calibration? I guess one other idea, which is a long shot, is how do the tube pins look? If they are dark and/or corroded that could be an issue (although it seems highly unlikely that all those tubes suffer in the same way). But you could try hitting the pins with very fine grit sandpaper to clean them up.
Again JMO/YMMV and all that, but I wouldn't pay NOS prices for "heritage" EL84s when you can get 6P15P-EV or -ER tubes for considerably less and they sound better.
Also, and again strictly FWIW, there are many threads about UFO power tubes and specifically EL84 vs. 6P15P. For example:
https://www.decware.com/cgi-bin/yabb22/YaBB.pl?num=1649456236