How can I install a frost-free outdoor faucet with very little space?
The purpose of the extension on a frost free faucet is to get the valve itself in a heated space inside of your home so that it could never freeze (see the below diagram). If you only have an inch or so of insulation that's being penetrated by these plumbing pipes, it's likely that the valve would still reach the freezing point inside of your wall. So any type of build out on the outside of your home to mount the faucet is defeating the purpose of the extension. The proper way to use this type of faucet would be to build out something on the inside of your home, which I'm guessing isn't possible, or at least unattractive in your situation.

Therefore, I'd recommend getting in the habit of shutting off the water on the inside, possibly replacing the shutoff valve with a quarter turn ball valve so that it's quick, easy, and obvious when it's been done. You want to open the outside faucets when the water has been shut off so that the lines are empty when they do eventually freeze. After they've been left to drain for a day, I cover my outdoor faucets with insulating covers. This is also a good time to drain the hoses and bring them into a protected location (e.g. a garage or shed).