I did exactly what you're talking about - away rotation through mid November and was fine. Was able to still get most of my interviews done in early December/early January. I took a day off to get to an interview elsewhere (similar geographic region) and it wasn't a big deal at all.
If this is a program you really want to go to, visibility on an away rotation is a good thing (I know there are differing opinions on this forum, but I strongly believe my away rotation was a big factor in why I matched at my top choice).
Just carry your phone with you, set it to vibrate w/ push email notifications and religiously check it when you're on break, not in cases, etc. to make sure you quickly respond to interview invites to get first shot at dates. If you have to hop off and do an interview during your away rotation it's not ideal, but I would just be honest with the program and say you tried to get a different interview date, would love to stick around with said program if they'd have you but ultimately have to successfully match. I have a hard time believing anyone would really give you grief for that.
Just make sure you read up on your cases, show up early and have Baby Miller (or insert favorite intro anesthesia book here) and make sure attendings/residents KNOW who you are and how awesome you are to work with. Rest should fall into place. Good luck!