Recent work by Burdman, Lane, and Rador has shown that B-meson mixing places stringent lower bounds on the masses of topgluons and Z' bosons in classic topcolor-assisted technicolor (TC2) models. This paper finds analogous limits on the Z' bosons of flavor-universal TC2 and non-commuting extended technicolor models, and compares the limits with those from precision electroweak measurements. A discussion of the flavor structure of these models (contrasted with that of classic TC2) shows that B-meson mixing is a less reliable probe of these models than of classic TC2.