Out of curiosity, have you read the Dunk and Egg stories? For my money, those are the perfect sorts of adventures PCs can have in Westeros without marking up the larger canvas. Granted, Dunk and Egg have far more important futures ahead of them, but at the time, the stories, the risks, and the stakes involved are all appropriate to an ongoing campaign.
“It’s a time machine, Superman. It doesn’t matter how long it takes to fix, as long as it gets fixed.”