I too have a Surface Book and have been having problems with Sony Screen Mirroring. For me, the issue is with a Blu-Ray player. Hopefully what I've learned so far might help you out though.
The biggest hurdle I got over is Windows Firewall. Don't worry about your router for now since Miracast (as I'm sure you know) doesn't use your network/SSID. So, search for Windows Firewall with Advanced Security in your Start Menu and click the hyperlink called Windows Firewall Properties. Go through the Domain, Private and Public tabs turning the firewall off. Then fire up Screen Mirroring on your TV, hit Win + P, then connect to a Wireless Display, then choose your TV.
Even though my Surface Book and Blu-Ray appear to connect at that stage, only the Sony default blue wavey background shows. Still, it seems like progress from having no blue wavey background.
Finally, you'll ideally want to figure out which port to open on Windows FIrewall, then turn the firewall all back on. Safety first etc.