Introduce yourself as soon as you get there, definitely ask about extra rotations or opportunities/ imaging on call or radiology journal club stuff etc. There is a Jan 2017 SGU grad who just matched at UTK for SA rotating - I can put you in contact if you are not already.
As for LOR - If you approach clinics with the right attitude, you will have several clinicians to choose from. I had a surgeon, a well known IntMed, and a Cardiologist. The cardiologist offered to write me a letter after his rotation, I wasn't sure then if I was going to apply. I asked the surgeon midway through my second rotation with him after a resident said "If you haven't asked, you should, he raves about you to the residents." I asked the DACVIM as a good third letter as he was respected faculty, and he gave me excellent advice on picking varied, not just IM if that was an interest, and making sure they knew my work and were willing to write me an excellent letter, not just a letter.
Remember, though you will only have 3-4 letters, many other faculty will be part of the discussions in the second week of January conference calls. So don't think you only need to impress your LOR writers, be fabulous at all times. I had a great case that ended up in the owner donating to the VMC in our names, and the IM doc I worked it with turned out to be head of MNs selection committee (and not one of my LOR).
deja vu? Congrats btw 
