> But I've played on keyboards tuned to exact just temperament in a particular key

Well, that's your problem. You're using a keyboard, which doesn't permit you to harmonize dynamically the way an unfretted string instrument does.

Even within a particular key, the pitch that sounds the best for a particular note will depend on which other notes within that key you're attempting to harmonize with. A keyboard can't do that.

Btw, this is from the wikipedia article on Equal Temperament, and I'd say it aligns with my general understanding/ expectation:

"Unfretted string ensembles, which can adjust the tuning of all notes except for open strings, and vocal groups, who have no mechanical tuning limitations, sometimes use a tuning much closer to just intonation for acoustic reasons. Other instruments, such as some wind, keyboard, and fretted instruments, often only approximate equal temperament, where technical limitations prevent exact tunings.[4]"

No and it's possible that as a pianist my ears are more attuned to prefer equal temperament than those of a string player. But I admit when singing a capella there are occasions particular chords just seem to sit better than when having to match a piano accompaniment, and to some extent that's likely to be the ability to use "purer" intervals.