I undertand how you're feeling, I think. For a long time, I was convinced relationships weren’t for me because I wasn’t willing to be physical/sexual before I was ready and the guys I was meeting were always ready long before I was. I wasn’t adverse to casual touching or a kiss goodnight, I just didn't want the first kiss to escalate to full-on body press with heavy breathing and massive amounts of tongue. And when I said wait, I like you but this is just too much too soon and my "date" said OK, understood, and we'll take it slower, I didn't want him to try the same routine again five minutes later. (And I don't think this is an exclusively male/female thing, but that's kind of irrelevant if you're a woman wanting to be in a relationship with a man.)
I find that OLD and other forms of organised "dating" are bad for people who are slow to warm up. I think these methods mostly attract people who want to be "in a relationship" fast, without a lot of preliminaries. They're meeting you thinking "will we hook up, yes or no?" or "is this my next partner?" not meeting you as a person and deciding if they want a relationship with you and what type. Many are meeting several "options" and out of the individuals they feel compatibility and attraction with, they're going to focus on those who seem enthusiastic about moving full steam ahead. And that may mean cutting out someone they do like and connect with to spend time with more of a "sure thing".
I don't know the solution, but I think you were on the right track with getting to know people without this huge focus on "is this my next Mx. Right?" Can you take the time you've allocated for dating and at least for a little while focus more on group activities that interest you, maybe something via meetup.com or a local group? Within the sphere of OLD, are there sites/groups that are more flexible, might include those who aren't only looking for insta-love? Can you put something in your profile about wanting to take things slowly, and look for profiles that say something similar? Maybe spend more time talking before you meet so the ones who genuinely can't handle waiting will know to rule you out, and you can rule out the eager beavers and the guys who get sexual way too fast for you (even over the phone/online)? It's not perfect, just some basic ideas.
He actually texted me this AFTER saying that he doesn't want to see me at this time: "How much nicer would it have been if we cuddled up in bed together?” This particular comment comes across as really self-centred to me. It would have been nicer for HIM, but obviously unworkable for you. He’s not taking your feelings or needs into consideration AT ALL, even now when you’ve thoroughly explained them. You've both decided not to pursue anything, but he still has to be universally "right" and make you "wrong". And he has to tell you that your way of dating is not "dating", but you'll come around "when you're ready to date". This fellow is all me, me, me - no compromise, no empathy, no idea that people legitimately exist and thrive while being very different from him. I’d try not to take this one personally, just use the experience to get better at spotting dickheads warning signs.