I face similar problems at my home institution, but having got a PhD I know different. The radiology department here is largely oblivious to the fact that we have one of the most well-known MRI research programs in the country. I don't want to be more specific than that, but if you'll take my word for it, I'll give you an example;
I asked a full professor in the radiology department (a PhD) which radiologist MD was doing research so that I could get some experience doing clinical research before graduating - he said there were few people interested in research and the junior faculty that were - that bascially I would be mentoring them! Initiating your own clinical research is certainly a possibility, but this is very time-consuming and one may not have the power to pull it off.
Anyway, we publish animal radiology research all the time, sometimes in clinical journals about important radiology questions, yet still very little interest from the radiology department!
So, maybe you should look closely at basic scientists at your home institution as well? Maybe there are animal magnets and work being done there that you overlooked? At several schools there are separate "institutions"/buildings away from the radiology department that do a lot of radiology research. These projects sometimes work much more quickly, so that if you helped out, you might get your name on an abstract before you interviewed. Of course if you're doing this largely for a letter of recommendation, I'm not sure one from a PhD will help (someone else would know better than I!).
Alternatively, maybe there are clinical radiology faculty at your home institution in a radiology area outside your interests, that have good research and would serve as good mentors (even though their subject is something you don't see yourself ever doing again!). The other sad fact, that personally concerns me for radiology's future, is that at many places, neurology and pyschiatry are often doing more interesting MRI research than radiology!
However, your impressions about your home department may be right. Here, I'm personally thinking of trying to do an externship at MGH, NIH and maybe go abroad for another different perspective. Of course, I'm gungho research. If you're a straight MD student the latter 2 options might be hard to arrange without contacts, but your first option (as you stated in your original post) might work.
Hope this helps!