This is certainly one important path. But people should be very wary of leaning too heavily on the "homosexual" mistranslation. Conservative theologians and religious leaders are smarter than that. It's not like they're unaware that the translation has its problems. And they don't rely on the translation for their moral condemnation of queer people. Conservative Christian scholars and teachers are quick to point out that Jesus was raised in a Jewish world, and that Jewish teachings of his time (not just Bible verses) were fairly condemnatory of same-sex relationships. Maybe Jesus agreed with this, and maybe he didn't. Some stories about his life (like the centurion and his beloved servant) seem to indicate that he didn't care a lot.

On the other hand, he was very explicit that following Jewish law was very important, and he urged his followers to do that.

That's what conservative Christians bring up every time this issue is raised. And they're unmoved by translation problems in Paul's writings, which they do not consider to be key to their theological positions.

The points you make here about the mistranslation are really important, but they're nothing like a decisive answer to the homophobia baked into Christianity. We can thank a recent film for overemphasizing the importance and making it seem critical when it really isn't.