Since aways are so important, why not do more aways for less time? I think you would be able to get an adequate look at the school and show them who you are as an applicant. Plus, if you realize that you don't like the school then you don't have to stick it out for a month. The only disadvantage that I see is that you may not get to know as many people there or be as likely to get a good LOR if you were hoping for one. But, I think you could get a good feel for a program. Thoughts?