Of course, a 6SN7 GTA can be a good fit in a given situation. It all depends on the other components of the setup, preferences, acoustics, etc. A SET or a PushPull have a completely different set of requirements, as the power transformer is already a source of timbre. An OTL is a completely different world; the sound has to come from the tubes. I've been working with these OTLs for about 17 years now, and my journey has also been one of trial and error.
As Pindac also indicates, a single-tube setup is simpler, but this comment deserves some qualification. With an MP-3, it's much easier to determine the character of a 6SN7 tube because it only uses one pair. But that's also its limit. My best experience there is with a Sylvania GT Bottom Getter (VT231 is still reasonably affordable), which delivers a lot but, to my ears, doesn't yet have the right timbre on its own in an OTL. Incidentally, the 12AU7 also plays an important role here, but a good, silent NOS is difficult to find. It's important to consider the power amplifier in your approach. With solid-state, it is what it is. But if you have an M60, you can further build on what the MP-3 delivers.
My strategy is to ensure the preamplifier is perfectly matched in terms of sound, spatiality, and detail with the right tubes. Slam and engagement don't play a (major) role in my approach there. I address those in the power amplifier. The more tubes in the chain that determine the sound, the more compositional possibilities you have to achieve the desired result. With a combination of an MP-1 Mk. 3.3 (latest update) and an MA-1 Mk. III, you have six tubes that significantly determine the sound. On the one hand, that's fantastic, but on the other, it presents a complex challenge.
Whether it's an M60 or another Atma-Sphere amplifier, based on my strategy, the engagement, slam, and experience (where you're sitting in the concert hall) should be created there. Regardless of which Atma-Sphere power amplifier model you use, I would recommend using a Linlai GT E and, in the case of the M60, completing the process with a second tube. With the MA-1, you have two tubes to do that.
Pindac rightly points out that not many have the necessary tubes for such an experiment, at least if I'm interpreting his/her comment correctly. But I think that if you have an MP-3/M60, and especially an MP-1/MA-1, such a setup deserves a carefully selected set of tubes. That's the corresponding investment. Not everyone will be as crazy as I am to amass a tube collection that now represents the value of a small car. But perhaps there are enthusiasts nearby who could borrow some things and/or try them out together. In the Netherlands, as a hobby, I'm willing to occasionally visit an Atma-Sphere owner with my tubes by appointment.