I use the 11" for Final Draft and I don't have a problem with the screen size. I do minimize the toolbars as much as possible and hide the dock, but that's a no-brainer. With those optimizations, I find I can see the better part of a page at 100%. The screen is wide enough at that point to also have a separate document (a script or maybe just my notes in a text document) off to the side. Obviously the additional screen real estate of the 13" would be welcome, but I do also appreciate how small and light that 11" is. Battery life on the 11" (it's a 2013 model) is upward of 6+ hours which is more than enough for a cross-country trip.
As far as the distraction problem — is your main computer a laptop? Because if it is, maybe do what I did. I set up a separate, really minimal user account on the Air, and also on my Mini at home — that account is named "Writing Only". No email running, no iMessage notifications, no Facebook. I'm less tempted to look at the internet for "just a minute", and if I need to use social media, email, etc, I have to make a conscious decision to switch accounts back to my main one, where all the distractions are there waiting.
Dropbox handles syncing of writing files between the accounts and between computers, so I never have any problem with versions. I encourage every writer to install the Dropbox (or Google Drive) desktop app so your writing files are continuously synced and backed up as you work. If you write offline, they'll sync up as soon as you reconnect.
