... When you are describing load resistance, am I correct that you are discussing the reflected load resistance on the tube? (which then a function of the mismatch/match of nominal resistances) ...
The speaker's impedance, reflect back to the tube by the turns ratio of the output transformer, is the only load the tube has. So yes.
... Others, one of the reasons I suggested the same model speaker, with different nominal resistances, is to minimize the effects different speaker models/brands have on tonal qualities.
That's splitting amoeba-hairs, because the change from 8Ω up to 16Ω or down to 4Ω is the overriding factor. All speakers are varying in their impedance with frequency; see any
Eminence data sheet for a plot of impedance with frequency.
... The speaker is 8 ohms and running it from the 8 ohm tap. Do you think i'd likely get a better tone in either smoothness or complexity by running a 16 ohm version of the same speaker off the 8 ohm tap considering the OT's primary impedance? Right now it gets a bit too thin and hard at stage volume to easily dial it out.
Who knows? Tone is in the ear of the beholder. If the amp sounds thin & hard with the rated 8Ω speaker, you may want to alter the amp rather than chase minor colorations from mismatching speaker loads.
It could just be the speaker itself. ...
Yes! Speakers vary enormously in their overall response, and the sonic effect isn't always obvious from frequency plots, etc. You need to hear different speakers with your amp to know which is the best fit. And if you have a known-ideal speaker, you may have to adjust the amp's voicing to work well with the speaker.
This video may be a starting point (it helps if you use very good headphones). The G12T-100 sounds at once meatier, but with a harsher sizzle, than one of the benchmark holy grail speakers, the silver alnico G12 at 3:39.
Or maybe
this video.