Tube type vs Wattage

Bjesien:
I do not believe one should buy an amp based on its power tubes. Input tube tube type, driver/phase splitter design , coupling caps, cathode caps and the factors mentioned by Atmasphere affect bass response more than the output tubes.
Above all, there is no substitute for auditioning the amp with your speakers.
Having said that, most EL34 based amps I have heard sounded midrangey to my ears, while 6550 amps are all over the place and KT-88 amps tend to have strong bass. This is all subjective opinion IME.
Personally, I would not buy an EL-34 based high-power tube amp, because it would certainly need at least two matched quartets of EL-34 tubes and probably will require a complex bias adjustment procedure every time a tube drifts.

Also, please let us know your speakers brand/model. Matching tube amps and speakers is not a straightforward calculation. More power does not necessarily mean more bass.
Good luck

Bjesien
Those are great speakers, congratulations!
They should be easy to drive with tubes.

You wrote:
" I once had a Mastersound amp in this same setup and it sounded like the players were in the room. It was a 300B and all but the bass was extremely satisfying."
This is the famous SET (single ended triode) magic. Unfortunately it is difficult to achieve tight bass with SET amplifiers, though the midrange is to-die-for.

If you want to try SET, I would recommend 845-based amps, they do much better than 300B amps in terms of power and bass control. 845 tubes do have wonderful midrange "bloom", it more than makes up for the slight lack in bass control.
Art Audio and Dehavilland make great 845 amps.
Unison and Viva from Italy also make great 845-based integrated amps.
IMO, avoid the cheap 845 amps on Ebay, there are several reports of weak bass due to sub-dimensioned output transformers.

If you want to stick with push-pull amps, I love the McIntosh Mc275, it sounds very powerful and "in-control", the latest version has about 90W/channel. Its bass is tight and tuneful after burn-in. It has great soundstaging and midrange. I regret that I sold my Mac, it is a great amp.
I understand it is available as an integrated amp with modern looks, the Mc2275.

I have no first-hand experience with VAC amps.

You wrote: "Looking for that organic 3D sound with more transparency than the VSi-55 and Tamino combination",
You may also want to audition the latest ARC Ref 110 amp, if your source has balanced outputs AND volume control. ARC amps do have transparency and soundstaging in spades.

A friend of mine owns a great class A KT-88 integrated amp, the Unison Sinfonia, 30 Watts/channel. It sounds wonderful, with very controlled bass and amazing soundstaging, specially when listening to vinyl. Class A watts sound very powerful, more like 60W in class AB.
I hope this helps