Translation:Nonetheless I do not want the tallest men.
I decided not to report it as an error, because I could not find "anyway" as a translation of "tuttavia" in any dictionary. So, strictly speaking, I don't think it is an error. It is just that it is a useful expedient to remember the literal translation and use that instead of a more widely-applicable translation. Thanks for the feedback :-)
Is Tuttavia non voglio uomini più alti correct for I don't want taller men?, as taller than an aforementioned height.
And Tuttavia non voglio gli uomini più alti for I don't want the tallest men?
For instance, in Spanish if I'd like to say the first one, it would be: No quiero hombres más altos and the latter: No quiero los hombres más altos