I too agree that July is a horrible time for all of the above mentioned reasons. However, I do suggest August as a good time to rotate through EM. If you are a strong candidate with a good step I score, this will allow you to study for and take Step II at the end of July, leaving plenty of breathing room to concentrate on the application and interview process. Likewise, it will (at most schools) give you the oppurtunity to get a meaningful rotation such as Senior Medicine in before you leave, keeping medicine fresh in your head.
Whether or not you do your rotation at a program you would want to attend is your choice. I did and it worked out wonderfully (I also did it at a "big name" program, which gave my CORD letter some extra weight in my application). Essentially, any program is going to assume you want to apply there if you took the time to travel and visit for a month or so. That said, and being the small community that EM is, you will be looked at as a potential applicant regardless of your desire to attend there or not, and your CORD letter of recommendation will reflect your work- not your desire to join their program. In short, if you are enthusiastic, motivated, and work hard (no breaks, pick up any unread charts as they arrive, and show a commitment to learn from your mistakes [you are still a student-not a resident yet]), I don't think you can go wrong anywhere, including your first choice.
I also believe that if you are planning on doing more than one visiting EM rotation, you should schedule your last one for November, which is typically the start of the interview season. This would also be a GREAT time to schedule a rotation with your first choice location. The first rotation in August will give you a chance to "warm up", and also give you a (hopefully) strong letter to send to every other program through ERAS, including the one you will rotate to in November. As interview offers are extended throughout October and November, you might be more likely to recieve an interview while you are doing your rotation, which will give you a leg up on the competition, and allow those inteviewing you to observe you over the month and really get to know you. You will find that as you interview at programs you didn't rotate at, you might sit down for 5-10 minutes with each person interviewing you, and not really get t know them at all. A month with the program you most want to attend will afford you the oppurtunity to (at worst) know that they choose you because of the way you worked - which probably meant you wouldn't have worked out well there in the first place.
Remember, scores, numbers, recommendations, and personal statements might get you into the door, but there is no piece of paper that can replace live, observed work ethic. If you are scared or unsure of your ability to perform well at the program of your choice, that is one thing, but EM is a field where initiative, courage under pressure, and cajones may take you further in the long run (as long are you aren't reckless). It is OK to be aggressive with your career plans, but be smart about it too. I was scared and VERY unsure of my abilities when I started my first away EM rotation. I left confident and secure that I have without a doubt made the right career choice for the rest of my life. In short - take the plunge, it will be worth it.
Just my $0.02...