After spending a bit more time testing my 5915 (6BY6) tubes on both regular "floater" and "strapped" EF95 setting and going back and forth a few times to compare, I can definitely validate my earlier subjective conclusions on sound quality and balance. Both settings yield excellent results, but the "strapped" mode definitely liberates the soundstage and makes it into a seemingly limitless field of sound, whereas the "floater" mode, while quite large, has a more intimate soundstage with instruments very well separated but squeezed closer together.
Floater mode is more immediately pleasing and euphonic, with great detail and realism, excellent separation and nice bass, excellent for casual listening; but strapped mode is a whole step above in terms of detail and the "being there" effect, and also has drier and possibly cleaner bass, not weaker than than in floater mode, and more treble and high mids energy. It sounds more balanced, whereas floater mode is a bit darker all in all.
Speaking of more treble energy, I have had some trouble reproducing the volume pattern that seemed obvious to me on my first try. While the strapped setting definitely is a bit louder for music, I am not sure that difference is still that relevant for weaker signals. On the strapped setting, it seems like I can turn the volume up about as much as I want without the sound getting immediately louder, but more like everything on the stage is just becoming more intense, more boundless and strong if you will. I was actually a bit bothered by this when watching a movie last night, as whatever volume I used, the audio was never loud -I mean it was still plenty loud though lol- but just intense and surrounding; realistic at any rate, as it sounds like you're in a room, theater, opera room or open field. Both settings require me to go very high -too high imo- on the volume knob to watch videos though, as I need to get close to 12 o'clock to get things even a bit loud (I need 10 with my 6AV6, which is quite a major difference!).
About the slightly higher perceived volume for music -loud signals- on the strapped setting, I think the extra treble and high-mids energy plays a large part in that sensation, in that, I might be getting a bit more volume but perceive much more because of that.
Anyway, don't panic because I mentioned treble energy; on my headphones, when I hear some powerful -not hot- high mids and treble frequencies and everything else at about the same level, it just basically means that I'm getting a very balanced sound originally; so you probably wouldn't even notice it with, say, HD650 or such; it would sound great on them actually, considering their "dark" nature.