Like PRR and others have said, the thing is with higher output SE amps is the cost compared to PP amps of ~ the same power.
Not only is a higher wattage OT much more expensive to get to 15w to 20w, but there is a considerable size and weight penalty.

But a pair of 6V6's and their OT can get you ~ 20w/22w for a lot less $$, weight and size.
And if you build a KT88 ES amp it's not going to sound very different than a PP ~20w amp if your playing on the clean side. To really hear the sound of that KT88 you have to push it into distortion. Will you be able to turn it up that much?
Not trying to squash you vision. It is a lot of fun to build an amp and you always learn things from building it, just want you to think it through.
I built a Princeton 5F2A, which is a Champ with a single knob tone control, think tweed Deluxe tone control. I wanted a lower output amp for at home and I wanted to/feel what a SE amp sounded like, and see if I like them. And like PRR and others have said, it's still plenty loud, sometimes still too loud.
I built it with a rectifier tube so I could change the dcv by swapping rectifier tubes, 5Y3, 5V4, GZ34. I wanted to hear the difference at different dcv's. I built it with a 10w SE OT that is made by Haybor, size/weight/$$ were just not that much more than a standard Champ type SE OT. I was running it through different single 12" speakers I have and through a single WGS alnico 15". (Always run through a Fender stand alone reverb clone I built.)
As you would expect, the 6V6/5Y3 breaks up the fastest and the 6L6GB-C/GZ34 is the cleanest. But the 6V6 sounds pretty different than the 6L6, wither both are clean or both are ~ the same break up, 6V6 is warmer/fatter/less sparkle, tried with both NOS and new power tubes.
Problem is the extra heat when using the 6L6/GZ34 combo, that steel tweed chassis gets HOT! in the tweed Princeton 12" speaker combo cab. Could be fixed with a small fan in the cab, even a small pedestal fan set behind the amp.
If I built a SE amp again, I'd go with SS rectifier and put in Power Scaling/VVR to adjust the output tubes plate/screen DCV. I can see a 2nd Power Scaling/VVR just for the preamp set up with a dc voltage clamp on the preamp tubes dcv, so as you dial down the power tubes dcv and unload the PT's B+ dcv, it clamps the peramp tubes dcv at where it's set, it doesn't let the pre dcv rise. And I'd want to build it to use 6L6 types including KT66 and EL34/KT77. Just to hear them.
I'd use a full AB763 preamp, with full TS including mid control, so 2 preamp tubes, probably have the input 12AX7 wired up to be either single or in ||. You would have several different options this way, like a 12DW7 in ||, which would be 1-12AX7/1-12AU7, or a 12AU7 in ||, or a 12AY7 in ||. A plus of the full tone stack would be to help eat up some gain from the 3 stage pre. A volume and and a master volume.
And the amp build I've been thinking about for several years would be a stereo SE 6L6 with the Magnatone stereo pitch shift vibrato. Get around 16w to maybe 20w? I have 1 of the new stereo Maggi's and it sounds wonderful to me, but it's 42w's with a 2x12"s stereo cab. A little much for at home
Magnatone does make a lower wattage stereo amp but it's EL84's and the 2x10" speaker cab has the speakers to close to together to hear the watery slap of the sound flipping speakers back and forth. You'd have to hear to know if you like it. I love it! Never heard anything that sounds like it, and a Leslie is a different animal, wonderful sounding, but a different animal than a Maggi.