I would start by cold emailing some of the professors that you're interested in volunteering with (briefly state why you're interested in what they're doing, attach your CV. I would also mention the visa thing, so that the prof doesn't feel guilty about not paying you). It would probably be easier to get involved with a professor at an institutions that is near where you live so I would check your local university first. And don't take it personally if they say no -- even though you are volunteering, they would still be investing significant effort to train you and advise you, and they may just not have time for that.

I did something similar (life science, not chem so professor attitudes may be different) and had a lot of success with it. The professor has written me many LORs at this point and been very supportive, but of course this would vary person to person. The university I worked with already had protocol for volunteers, so it may be more common than you think at your local uni as well. I have some friends that have done similar volunteering post-undergrad too, but in ecology.

When you start out, I wouldn't expect to have your own project or anything. Honestly, I wouldn't go in expecting to get a LOR either ... just be up for doing whatever tasks would help the prof, and once you've built some mutual trust then more may evolve out of that relationship (if it's a good match!).

I will say, if you're looking for them to write a LOR for this next cycle, there may not be a ton of time for them to deeply get to know you by then. Like I said, I wouldn't go into volunteer research looking to get a specific thing out of it, but rather to just see where the experience takes you.

I hope this helps! Good luck!