Porty/Craigmillar is probably best bet.
I find Bruntstane Road awful and avoid at all costs, especially going up (south) when I'm considerably slower that the often impatient drivers.
Would suggest having a look at either:
- Footbridge over to Hope Lane then through Magdelene.
- Brighton Place, Durham Road, and through Bingham (Brighton Place not great but rest v. quiet residential streets)
Getting very circuitous, but from Forkenford on The Innocent you can cut through via a path to King's Haugh Industrial Estate and then some shared use path on Peffermill Road to a path that then heads over to Bridgend - off road all the way to ERI from that path.