It looks to me like your problem isn’t that you are an introvert. Your problem is that you don’t give people much of a chance. For every possible avenue for meeting people that you mentioned, you had a reason why it wouldn’t work. I assure you: Not everyone at the gym, the church, or any group is the same. Every person is as unique as you are. Yes, some people simply won’t be a match. But I’m reasonably certain that in any group of people there is someone much like yourself who is trying to decide if you are approachable.
Focus on the activity, not on your goal of meeting people. Find something to do that will add meaning to your life and that attracts people who are about your age. Volunteer for a cause you believe in. Take some kind of lessons like dancing or join a singing group or hiking club. It doesn’t matter what you choose as long as you have some genuine interest in it. Then go long enough that you give yourself and other people a chance to get comfortable. It will enrich your life and increase your social options.
I wish you well.