I've been using SET amps for over 20 years but didn't originate my interest via the SET cult community. My speakers are 101db/w/m, so several db more efficient than PAP (which I've heard), depending on which version and vintage of the Trio 15 you have. It's true that a competently-designed and built 2a3 SET amp can produce truly excellent bass character and with Joourney-to-the-Center-of-the-Earth excavating depth. It's easier to get uncompromised deep bass out of a 2a3 than from a 300B design, generally. But when people say that 4-6 watts of triode power is perfect for a 90-96 db/w/m/ speaker, you have to start querying their true listening habits, particularly for how much they value dynamic life in their music listening, and then actually indulging in it. I don't know where you are, but for example, a Tokyo-dwelling SET / hi-eff speaker listener espousing the perfection of 2w 45 SET amps or 4w 2a3 sound, has to be inferred considering his or her context. They may have much different priorities than you.
In other words, a great 2a3 SET amp can qualitatively deliver convincing bass through your PAP trio 15s, but will it be musically-convincing if you value dynamic life in your music, and sense a looming ceiling on headroom? That depends on you, your room, your habits and expectations.
I stopped trying to get rich sound out of KT88 tubes 20 years ago. There is just something there that puts a little grit and gloss in sound that doesn't belong there. KT66 is more interesting and musical, along with its 6L6 counterpart, and of course the venerable EL34 when you can find good ones. I am not surprised you find your 811 amp too thick. I think for your speakers (what are your room dimensions?) a better combination of power and single-ended incisiveness is likely called for. You mention you don't want "lean and clean," but instead "warm and clean and accurate; truthful to the source." But isn't there a contradiction in that wish? "Warm" is almost never truly accurate, but it is euphonic. Can "warm" be truthful to the source if the source is "cold" or "lean and clean?"
I find that a well designed 2a3 push-pull amp can really help here. You'll get about 13 w, bass can be phenomenal, and if the design is simple, it will be absent the subtle grit of crossover notch distortion. But if you want that 4w purity with more oomph, you can have a 2a3 PSET amp built for roughly the same output. You need the amp to have an oversize power supply and simplicity for fast, agile, communicative sound. You'll get enough warmth without the bloat common in many (not all) 300B implementations.
845 amps provide another path for SET with much more shove. Not long ago, most 845 tube options brought anywhere from a little to a lot of thickness with them. That's been changing. Psavane, Elrog and KR have exotic (and expensive) options. But Tube Amp Doctor has the relatively new Shuguang 845C Iron Plate 845 built for 95w dissipation rating. The earlier 70w dissipation 845C metal plate had a bright, fleet-footed voicing but many 845 amps had to be re-biased for it lest it cherry with short life. The new iron plate has higher heat dissipation and can be dropped into almost any 845 amp. It is noticeably quicker than the 845B and other graphite tubes, and when combined with an intrinsically fast and transparent design like the Audion Black Shadow, it delivers a particularly objective sound.
Another option is something I haven't seen on the market yet but which I am thinking about commissioning. The KT150 tube is the best sounding of the modern production kinkless tetrode tube designs I've heard. A single-ended tetrode amp using the KT-150 should yield a solid 25w. Paralleled, you can get to 40-50w. Push-pull, 60 - 75w. Single-ended pentode-and tetrode amps can resolve the conflict between SET purity and pentode/tetrode push-pull compromise. And you get some interesting alternatives aside from KT66, EL34, 6L6. The NOS German EL156 and F2a are particularly interesting for their combination of bandwidth, linear performance and exceptionally long life for power tubes.
But I fully understand if you want to stick with SET. Before you commit to 4-6 watts via 2a3 SET, understand the priorities of the person recommending that, and find a way to listen to your system, in your room, on music that is vital to you, to determine whether it works for you. For me, on 101db/w/m speakers and a 21'x14'x8.5' only partially bounded space, a 4w 2a3 SET amp is one tool in the shed. But most of the time it would be benched, because the headroom ceiling is palpable on highly dynamic music.
Phil