But if I start off fairly certain that there's nothing wrong with same-sex romance but am also looking for some sort of theistic tradition that makes sense given what I already know, then Catholicism's views on sexuality would seem to count against it.

Depends on how strong my evidence is for this position. If it's nothing stronger than "I can't think of any reason why same-sex romance is bad", then it doesn't take much evidence for Catholicism to overcome it.