Do you think it's worth it to email the different institutions to at least get my name out there and show interest?
The irony here is that I tried the exact same thing, but I didn't get any response....except for one generic "check on our website." Chances are that the hiring guns don't really have that time. You can also imagine hundreds, perhaps a thousand others like you sending a similar email. And the concerned job market is also a major player here.
However, regardless that it is likely to be a waste of time, go ahead and do whatever you think might help. That it didn't work for me, or any other person does not mean that you may not get lucky. After all, what have you got to lose, right? Doesn't hurt to try....not in this case anyway.
At least, try to leave a memorable impression at your rotations. This will make it easier for preceptors and/or pharmacy managers to give you a decent recommendation, when you list/use them among your references.
Another strategy I have seen work in the past is to convert any or some of them (preceptors/managers) into an ACTIVE/RESPONSIVE/EFFECTIVE mentor(s). Make sure he/she is reputable & competent. Otherwise, his/her input will be of little to no worth to you; as you may have heard, "pharmacy is a small world."