Run it around the edge of the rooms and if you have any issues you're not ripping the whole thing up.
If you can run on kitchen cabinet walls you'd never know you'd been in.
The kitchen kind of sits deeper than the other rooms so they'd have to under the tiled floor and either around a peninsula or under it. No reason why it couldn't go around the edge of the room after that though. Skirting would have to come off but that's not a big issue.