That's why I don't prefer tubes: too much hassle.
If you know what to listen for, and thrill to the sound of live music in a real venue: nothing beats tubes. Any equipment(tube or SS) takes time to sound it's best. Taking the time to burn in gear, and taste various tubes, is an act of love for some of us. Skydivers(I) have a saying: "We that dance are considered crazy by those that can't hear the music." Harley riders(I) have another: "If I have to explain- You wouldn't understand." Oil-filled caps will usually have somewhat of a fuller, rounder midrange(ala Mullard tubes, for instance- which some like), than would most film/foil caps(polypropylene/copper foil probably being the other extreme). I'm not certain about the burn-in time.
In my experience the BAT tube gear sounds very tubey and bloomy and that is what some listeners prefer about them. Also, BAT has for years offered the NOS variant tubes you are referring to as a desirable upgrade option.
My experience with those tubes suggests that they indeed may make the sound even more rich than the stock leaner sounding Sovetek 6H30's, pushing the already tubey house sound even further in that direction.
If you are looking for more neutral sound try an ARC or VTL piece instead. Otherwise returning to the Sovtek tubes will at least cause the sound to head in the other direction.