The enclosure is a great idea.

Also a screen in room would work too. I've done that before, leave the back door open for them so they can go in and out of the house all the wanted. Husband wouldn't go for a cat door there, but maybe you can do that instead of leaving a door open all day. I know not everyone can leave a open door like we can, the advantage of living WAY out in the country. He did build a nice wide shelf though, all around, for them to sit and watch the world.