I think a summer externship would not only provide you with exposure to different aspects of PM&R (TBI, SCI, In-patient vs Out-Patient, Sports, MSK, EMGs, etc.....) but also give you good connections for residency. An LOR from a private physiatrist is good, but an LOR from a PD or a professor would be better. Also, you will get more exposure to residents, and will be able to pick their brains. Of course, if it is cheaper or more convenient for you to rotate with a private physiatrist, that is better than doing nothing. hope this helps