Paul, I will preface my answer with the statement that due to the breadth of the hobby, one would think there are more pure pentode push-pull amplifiers available than I know of. But, the only two I can say with certainty are the legendary Quad II, introduced in the 1950s/reissued in the past decade, and the Audio Note (probably the most SET devoted tube amplifier manufacturer) L4 EL34 kit. For differing reasons, however, neither make much power. Obviously, we can all rattle off a list of current UL or triode tube amplifiers as long as a gorilla's arm.
The famous Scott 299 and later variants of the more ubiquitous 222 employed pentode operation. The evolution of the latter, in shifting from ultralinear to pentode, infers some definitive rationale.
Interestingly, the Quad II features the cathode cross-coupling Ralph touched on. Coming from a man who threw around such compliments like manhole covers, Bud Fried's oft repeated statement, "Peter Walker had a first rate mind" is indeed high praise. I'm not sure if their original design, the postwar Quad I did or did not; I don't know much about that product. My Jadis DA30 and DA60 (but not my JOR) do as well, though one could argue it's a slight bit different.
Larryi, the issue your friend described regarding PSE design is the common criticism of the topology. Still, my feelings mirror yours regarding your amp, I like the end result - the sound.
Being the former importer, I was fortunate enough to extensively compare three versions of a commercial 300B based amp: an 8 watt SET, a 15 watt PSE, and a 20 watt PP. Echoing my previous post, the SET simply did not have enough power to partner with a full range loudspeaker. The PSE gave up a little in the way of why people become smitten with SET, and though I still felt it was power shy, some disagreed. The PP was arguably adequate in terms of power, but a lot of the magic was sacrificed. Still, as I mentioned, the triode push-pull option is often an excellent one. In fact, of the line I represented, I felt their lowly, overlooked, affordable 11 wpc PP 2A3 was one of their best products regardless of price or status.
One huge point which needs to go along with any discussion of amplifiers is that a system truly represents a marriage between amplifier and loudspeaker. Of the different types of loudspeakers I have - typical ported dynamic, planar, front-loaded horn, backloaded horn, and true TL (I cannot speak to ribbons such as the Apogee), some of the partnering amplifiers I have/had (SET, PSE, OTL, PP triode, UL, or pentode, and SS) can drive them well, some can't. The ability to put power into a loudspeaker often transcends WPC or the loudspeaker's published sensitivity and impedance specifications.