Non-affirming Christians seem to have very few responses for their teen that comes out as gay, that will come across as positive and supportive.

That's because there are none. There is simply no way to say one's sexuality is intrinsically disordered without attacking their personhood. The only option is to erase the sexuality (celibacy), or change it (conversion therapy/entering a heterosexual relationship).

How can non-affirming Christians be more supportive of their LGBT teens to ensure that their mental health is not compromised as a result of homophobia and/or feeling ultimately unaccepted and unsupported by the very people who should be trusted to give them the most unconditional love?

They should undertake the hard and sanctifying work of changing their views, repenting of their homophobia, and affirming healthy relationships. This is the only way.