If you have any current ideas for an adaptive outdoor sporting equipment, that could be field tested during your research month, that would be a great research project that could possibly be feasibly done in a month. You would need to do much legwork with respect to 1) developing a prototype to test, 2) identifynig athletes to test it out 3)develop an evaluation tool to measure what outcomes you are interested in (e.g. 5 point likert sacle), 4) hopefully be able to quickly make new versions to retest in the same month if you only have one month of research.
I know you are doing this for altruism, but if you develop new equipment, you should look into your medical school's rules regarding patents. Where I am, I think students retain all patent rights, should you decide to pursue a patent. You may feel uncomfortable doing this since you are currently trying to find a mentor willing to work with you, but if your ideas could make money, you need to decide early on with the mentor how to divide the patent rights (could cost several thousands of dollars). If you don't think it will make money or have no interest in patenting it, then you can let it go. However, understand that for any company to want to mass produce any product there must be a financial gain (or at least break-even for nonprofits unless you get a large endowment)
Doing all these things in medical school (developing an equipment, testing it with a research project, getting a patent (this could look great, but could also make you appear to be greedy to the "academic physician not familiar with patent issues")) would look great on your CV.
If you are interested in sports medicine, keep in mind Mayo Clinic which has a great PM&R outpatient sports medicine program or Michigan State University fellowhsip. Unfortunately I am not familiar with programs that work with adaptive sports teams.
Unfortunately I have to work on a manuscript resubmission and data analysis for another paper so I will only check this site sporadically.
