@amir - I've tried the Gordon Terrace to Liberton Road, left, then right into Gilmerton Road, and it is indeed terrifying at times.
The option I take is a modified 1 Gordon Terrace to Esslemont Road, then immediate right into Liberton Road.
Sounds similar, however I've found a line that allows for a safe right turn at the lights, protected from both streams of traffic by other vehicles.
Basically, you snuggle alongside the oncoming right turning traffic, so effectively you sit in the tangential gap they've opened up between the right turning lane and the straight ahead lane. Go far forward, effectively to the lane dividing line southbound for Liberton Road/Craigmillar Park.
You're protected from the rear by the right turning vehicle to your left, and can see along the right turn lane for a clear gap to make your turn.
When you do make your turn, you are turning into the bus lane, and any drivers waiting behind you can turn into the general traffic lane simultaneously.
I'm happy to demonstrate this one if the above isn't clear - I've even begun to consider this "sitting across the oncoming right turning lane" approach for turning right down the Royal Mile at the Bridges - previously I've been scared by being sandwiched between two double streams of vehicles, however whilst there are indeed two northbound lanes at this point, there is only one southbound lane, the outer one being right turn only. By blocking this lane for southbound traffic, I'm clear of the northbound traffic and have just one stream of southbound traffic to cross.
Still in an experimental phase for the Royal Mile junction, however I'm now confident enough of my Liberton Road line to let my eldest execute it unattended - something I wouldn't do for the other right turn.
I'm ruling out the Kirk Brae options as that's a pig of a climb, even to Double Hedges Row, with impatient drivers expecting to get past...
Robert