The only SE amp I listened to was through a CD player plugged into the RCA input on my late 1940's RCA AM/FM table radio and it had a great nice midrange, and you could listen to it for hrs without fatigue. I imagine a better output transformer and a full range speaker would extend the bandwidth greatly.
It had a 6V6 output tube , but you only get 2W, so many go for a bigger PS trans. for a higher B+ which you need for the higher power bigger tubes.
Just from reading I don't think the EL34 would be my choice as it looks to me from my reading that the highs and lows tend to be rolled off and it has more distortion than I would like. Maybe on the lower price end the 6L6 might be what I would try, with the KT-88 on the high end. You would have the highest power potential with the KT-88 also.
PS transformers as you have gathered depend on the Output Tubes. George lists some that he used. Others have used Edcor.
Output transformers depend on the budget as the bigger usually have sonic advantages , but are costlier. Edcor looks to be popular on the low priced end with the 15W GX series the lowest I would go with the big 25W CX ones maybe a nice choice.
The bigger one will certainly give a more bass, but maybe not highs.
He mentions the Transcendars (He sells on Ebay & has a web site) as his next choice with Electraprints at the top.
He never tried the sometimes pricey overseas brands that can be great also.
Anyway the Edcors have UL taps which you want with his circuit as an option, and you should make sure any other brand you pick has them.
He seems to prefer a 5K primary for the transformers which is a good compromise between power and sonics. You can use 3-3.5K , for a bit more power, but you get a little more distortion.
Sure lots of reading out there on choices for SE or SET Output Transformers & favourites.
Sometimes you can pick up a good pair of used OPT's for a great price on AK, diyaudio, AA (audioasylum), canuckaudio etc. also.
Hope that helps!
Randy