Jwm you mention that most OTL amps sound lean to you. Have you listened to any of the Joule Electra models? It seems that Jud Barber has somehow managed to capture the harmonic realism so apparent with most SETs without any loss of transparency, the best of both worlds.
In my experience the perceived limitations by some concerning OTLs rest elsewhere in the system providing the speaker impedance/amp are a good match. A poor recording will really highlight problems more so because of the wide bandwidth performance of OTLs.