In my case, it was a requirement that I spend like 40 hours doing volunteer work at a homeless shelter or similar for a class on homelessness and public policy. The class was online through a San Francisco college but I was in Fairfield, about 45 miles away. So folks actually in SF had a list to work from to seek internships. I had to find my own if I was going to do something local. I went and asked to speak with the director and explained that I needed this for the class, when I could be there, some of the things I could offer, etc. I had to get a drug test before they would say "yes".

Since you don't need this for a class, you will need to be a little more convincing. "What color is your parachute" may be helpful in that regard. I would go talk to the guy in charge and tell him what you have told us: "I really want to do X with my life and am changing careers. Your company is the only one in the local area doing stuff I find really interesting. I would love to have the opportunity to spend time here and learn from people who are smarter and more experienced than I am. I am willing to do whatever you need done that will let me spend time here. I am willing to do so without pay if there are no current job openings for which I qualify. Is there any way you would consider letting me do that?" It might also be helpful to mention that you are aware of monthly meetups but scheduling conflicts do not allow you to attend. You should be prepared to state what times you are available and how many hours per week you can commit to this. If turned down, be very gracious about it and thank him for his time. If you do get turned down, if possible, close with "Keep me in mind if you change your mind/if something changes/whatever the appropriate remark is for how the conversation went (ie the stated reason for saying no)."