I agree that your personal story is important and you should tell it.
I don't think you're going to get anywhere trying to convince other Evangelicals that they're wrong about the homosexuality rules in their interpretation of Christianity. The thing is, people cling to religious dogma for deep-seated emotional reasons and aren't swayed by facts, logic or reason. The reasons are usually a combination of peer group pressure (more specifically, fear of being rejected or even persecuted by your own community) and fear that death is the end of your individual consciousness and there's no afterlife. This is why I completely gave up on the whole creation-evolution debate years ago and won't touch it with a ten foot barge pole*, in spite of having a human evolution themed blog. People will stop clinging to religious dogma when they want to do so. In the meantime, they'll cherry-pick and twist evidence to fit what they want to believe rather than approach it with a rational, open mind and go with what the evidence actually says is more likely. People who actually take this logical approach don't end up being Evangelical Christians or any other literal bible believing sect or other ultra-dogmatic religion (like Salafi Islam, for example) because they're not logical religions. They're more likely to end up being in a much more flexible and intuitive religion that gives them room for forming logical opinions like believing in Evolution or believing that the Bible is a historical document and Jesus (or Muhammad, or the Buddha or whoever) was a great guy, but they don't have to believe it literally. Or maybe they'll end up agnostic or atheist.
*okay, I have
one cartoon on my blog that mentions the debate but it's not there for the benefit of anyone who doesn't already believe in evolution.
On that, I'm guessing that you didn't change your opinion on homosexuality because someone sat you down and showed you how the texts actually don't support homophobia, even though they appear to. Much more likely you connected with someone's story, or you were disturbed by how much gay people were being made to suffer and had doubts about whether a religion that's supposedly founded on love could do such a thing - emotional reasons. Empathy is a vital emotion that should influence our decisions when it comes to the welfare of other humans. That's what it evolved for. So I'm also guessing that upon having this emotional conviction that persecuting people for being gay is wrong, you then went to reexamine the scriptures and realised that they're not actually as straightforward and clear-cut as your community has always made out. Hence the decision to go and tell them this and make them stop persecuting people. And it's probably a bit like banging your head against a brick wall - that's what the creation-evolution debate felt like - as all their ego-defence mechanisms come into play and they cling to their irrational belief tightly, no matter how many well reasons, logical, fact based arguments you present them with.
Because of this, I think you'll do far better with a blog that appeals to emotions. The basic fact that Jesus, who had a message of love for all humanity, wouldn't support persecution of anyone. You also should probably accept that a big part of the problem you're facing with Evangelicals is that it's not a rational faith to begin with and you'll get a good reception with Christian denominations that don't require clinging rigidly to an particular English translation of a book that wasn't even written by Jesus* and with non-religious people and with people of other non-dogmatic faiths. I also think your voice is important for anyone who's LGBT+ and stuck in an Evangelical family/community. It might give them hope that they're not going to have to spend their whole life surrounded by bigots, or having to pretend to be someone they're not in order to not be persecuted.
*King James wasn't a very nice person. He was known for torturing and persecuting people who were the wrong kind of Christian, so it's not really all that surprising that people who believe that the KJV is the literal, unadulterated word of God end up persecuting people based on rigid dogma.
I'd advise not bothering with trying to convince anyone with logic, facts or reason, or pandering to bigots (such as using the same terms they do - as per the previous comments about the use of the word "homosexual" etc) - just stick to the basic fact that persecuting people is wrong and your personal convictions. I think you'll sway more people that way and connect with lots of people who've already been swayed.