An interesting thought experiment - the best route for an inner ring road. Mind you, it would probably mean upgrading what are now some quieter streets.
We've got most of the northern bit already, Harry Lauder to Seafield to Queensferry Road. Then ...
Clermiston Road to Saughton Road to Longstone/Ingles Green Road to Slateford Road to Craiglockhart Avenue to Glenlockhart Road to Greenbank Drive to Morningside Road to Cluny Gardens/Charterhall Road to Blackford Ave/West Mains Road/Esselmont Road to Cameron Toll to A6905 to Duddingston Park Street back up to Harry Lauder Road.
You'd have to create a link from Clermiston Road to Saughton Road, bash through some heritage Corstorphine, no big deal. Upgrade the rest and allow access into but not through the center.