Great work on the route.
As mentioned above, you could cut a corner off the main road route through Edinburgh by taking the Roseburn cycle path from Silverknowes down to Haymarket (which worked well on the WH1000) rejoining the currently plotted route at the National Library. The disadvantage would be getting around Haymarket and up to the Grassmarket, which is probably a bit harder to navigate if you don't know roads, and you would miss the views on the existing route up The Mound.
I really wouldn't worry about cycling through Edinburgh, however. It's a city, and the cycling infrastructure in the centre is not great, but it's not a big place, and getting through the town is a pretty small part of the overall experience.
One (very minor) point about crossing the Forth Bridge; rather than cutting through the hotel grounds at the north end of the bridge, I would recommend staying on the cycle path to join the B981 north of the hotel (and rejoin the bridge the same way on the return). This takes you directly past the pedestrian crossing point at the north end of the bridge. There are cycle paths on both sides of the bridge, but typically only one of them is open, while they work on the other side. If you use the west cycle path exit to the B981 to leave and join the bridge, it doesn't matter which path is open in August next year; you can just cross to or from the appropriate side at the pedestrian crossing.