I hesitate to post this because I am not interested in being hit on and I am not interested in adding to the pile on of people criticizing you. But I spent all this time writing the damn thing. Sigh. So here it is, fwiw:
You know, I have gotten a crapload of rejection and hostility in recent years, not in a dating context but in another social context. So I am very familiar with how hard it is to remain open and do the zen thing and say "Those 5000 other catastrophes don't matter. This is a new person and what they think has nothing to do with what all those other people thought." But it sounds to me like that's a big part of your problem. In fact, you remind me of another man I used to know.
He was average height (slightly taller than me even) and he was convinced that "being too short" was part of why he had such a hard time getting a girlfriend. I had the worst crush on him (and my ex husband was shorter than me and he knew it) but he would not give me the time of day. He was toxic and mysogynistic and harped incessantly on how badly women had treated him. He did so in a manner that was incredibly ugly and blaming, like "all women are bitches" type attitude. To me personally, he was rude, hurtful, and talked incessantly in front of me about what he found attractive in a woman and did so in a manner that just screamed "Gee, Michele, you are such a fat ugly cow you ought to just have your vagina removed since it will never see action again".
I really liked him and I understood why he was so bitter, so I tried to get him to talk to me anyway. At some point he got irritable with me and basically told me I was wasting his time and that he would be willing to talk to me if he thought it might go somewhere. For me, that was the final straw. I gave up. I still had the worst crush on him but concluded that if he was the last man on earth, I would get a girlfriend.
You can't change your height. Yes, for many women, your height is a dealbreaker upfront -- just like for many men, a woman's age, weight or bra size is a dealbreaker upfront. Both genders can be equally shallow and asinine. The trick is to find some way to set aside your hurt and anger from previous interactions and not hang that crap on every new person you meet.
As for dating sites, I don't use them. But then I jokingly say "dating is against my utter lack of religion" generally, whether online or off. It is not my cup of tea. I don't have a particularly high opinion of the dating paradigm to begin with. It strikes me as a meat market approach. I think it is an especially poor fit for folks who won't "measure up" to whatever arbitrary norms most people are sorting by. I know I don't fit that mold either. And I won't accept being treated shabbily because of it. Men who think I am too old or too fat or too flat chested aren't the sort of men I want standing next to my fire anyway. Frankly, they aren't worthy.