“Homosexuality” is really not much different from any other sinful temptation. As such, I’m not sure anyone can really “escape” it, or be “delivered” from it.
Yes, people can find their same-sex attraction (SSA) diminish over time.
And yes, certainly people who experience SSA can refrain from engaging in homosexual behavior.
I just don’t think it’s helpful to talk about “escaping” homosexuality, since we don’t magically “escape” any other kinds of sinful temptations.
(I also think, FWIW, that the term “homosexuality” is so imprecise and unhelpful. Let’s instead speak of SSA and homosexual behavior.)
I think you’re looking at it from a purely secular, therapeutic viewpoint. Jernigan’s testimony is that he had supernatural intervention, which certainly CAN entail complete, or even partial, delivery from a compulsion.