I used to commute to Bush, when living in Morningside and later in Newington, so have used something akin to both the "Balanced route" (I didn't use Kirk Brae, just went straight up Liberton Brae, also I didn't turn off at Straition, just followed the A701) and the Fastest route. Personally I prefer the "Balanced route", but going up Liberton Brae and following the A701. Oh and I don't understand why it has a strange loop at the end, just take the road straight ahead at the Bush Road cross roads.
If I was using the fast route, I wouldn't bother with Seafield Moor Road, it looks a better option on the map, but on the ground it is narrower and has a lot of heavy lorries going to the tip.