Late-stage potential adviser contacts

[biblio_filia]

  Since I'm applying for Ph.D. programs in Art History, all of my applications are due on or around December 15. I have an appointment to meet with grad students at one of my schools in two weeks, but only one of my other schools is realistically geographically accessible. I have contacted a potential adviser there, but he proposed an extremely specific meeting time and date that was out of the question for me. I politely suggested that we might choose another time to meet, but I have yet to receive a response. Additionally, one of my former undergrad professors has told another professor in my area of concentration at the same school that I'll be applying there. Here's the issue: I have a ton of academic commitments, not to mention assignments, this month, and I can't spend any more weekends away. Should I still try and and establish an e-mail correspondence with one or both of these professors? And if so, what should I say? I would like to discuss the department with them, especially since I'm beginning to doubt whether there will be a strong potential adviser for me there.
   Should I try e-mailing potential advisers at distant schools, as well, even if there's absolutely no chance I can meet with them in person? One of my schools in this category actually asks whether you've been in contact with anyone during the application process, making me think I should be. I'm just a bit concerned about having nothing of substance to say other than that I think their research interests seem to match up with mine, and about the fact that time is short.

Thanks in advance!