Edit:
To make it explicit, here are some ideas:
1. Medical research institutes: Weil Cornell, Salk Institute, Mayo Clinic, U Texas-MD Anderson, Cleveland Clinic, UCSF, U Pittsburgh Medical Center, Oregon Health & Science, U Wash Medical Center, U Minn Medical Center, University of Penn, Harvard/MGH, etc.
2. Energy-related labs: Argonne, Oakridge, Pacific Northwest, Lawrence Livermore, Lawrence Berkeley, Los Alamos National Lab.
3. Other national labs: Defence research labs, Army Research Labs, AFRL, Office of Naval Research, Woods Hole Oceanographic, Naval Research Applied Research Labs Austin, TX/Penn State, Georgia Tech Research Institute.
BIDS actually recruits software engineers, some are working in OSS exclusively. Since they are in Berkeley, I would drop by and interact with them, they might have some insights for you.
That may be hard without a bachelors degree, prior research knowledge, and potential academic recommendations.
One way to short-circuit this is to take your software engineering skills to a research lab and work as a research assistant.
This allows you: a) contact with academics who are doing research b) the visibility of what research actually is c) to add value from day one
Most labs are in heavy need of software engineers to help with software related tasks.
So first focus on what type of research you are interested in (look at as many research labs in as many different disciplines as possible) and then contact them to see how you can help.