I say out. Hubby and I did a three-year long-distance dating relationship (him on the east coast of the US, me in Germany) culminating in marriage, and it never looked like this. I am a child of poverty, so I really get his shyness around your parents because that is what I was like with my much-wealthier, much-better-educated in-laws until time and some loving family stories from my MIL corrected all of my faulty attitudes caused by growing up dysfunctional and poor. But your guy has deeper issues.
I believe you when you say he is sweet - I find most people are. But that is not the issue here. Control in that degree is therapy-necessary, and I would not have you put yourself in that position so young in your life. I married at 26, after a few years of being out on my own, which I think is almost-necessary today regardless of how two people plan to structure a life together. You will be much more wise and mature. Your willingness to see the positive sides of him speaks to your huge heart, but you do need to protect that heart and yourself - you gotta trust us on that one. The better-balanced guy that is in your future will show you what a healthy relationship should be like.
If you do decide to stick with him, though, I agree with previous posters wholeheartedly - therapy for BOTH of you, no excuses, and if he won't go, then RUN!! I don't have the space enough here to tell you the stories of how I know this to be truth.
I have a mantra that I have spouted for years... "If I eat right, I feel right. If I feel right, I exercise right. If I exercise right, I think right. If I think right, I eat right..." Phil-SC