I walked the JMW in 2024.
I live in Edinburgh and offer this as an alternative route from Barnton to the Union Canal. I don't see the attraction of walking through Balgreen and by Saughton Prison to get to the canal. It seems a very long round about way for a shortcut to me and you'd be very hard pushed to call it scenic. This route is quicker and almost all off road along the route of old railways.
Amend the route from stage 4 of the Walkhighlands notes as follows. When Barnton Avenue meets East Barnton Avenue take a left to continue on Barnton Avenue. Don't follow the Walkhighlands notes and continue on East Barnton Avenue. A couple of minutes walk will take you to the end of Barnton Avenue where it meets Cramond Road South.
About 100 metres to your right is a Tesco. Cross the road and aim for Tesco. Follow the access road into the car park at the rear of Tesco. At the far end of the car park there is a clear and obvious path.

Follow this path for a few minutes and pass under a bridge. Once you've passed below the bridge turn right and that's you on the Blackhall Path. This is all signed at the bridge.

Follow the Blackhall Path - an old railway route - for about 20 minutes until you come to Craigleith. If you want to visit the shops at Craigleith cross the road and go straight ahead, it's about a 1 minute walk to the shops if you need a refreshment break/toilets.Craigleith is a path junction. Path to the left takes you to Crewe Toll and places like Leith. But you want to take the path that goes to the right, the Roseburn Path. Again this is all signed.

Follow the Roseburn Path - again an old railway so clear and easy to follow, no navigation issues - for about 15 minutes and you come to the bridge where it crosses over the Water of Leith.

Nice views up and downstream from this bridge. and from there it's about another 5 minutes to the end of the Roseburn Path.
At the end take the path that goes down to the right to Russell Road. Turn left and walk a bit less than 100 metres along the cycle track at the side of Russell Road, going below the tram and railway bridges. At the junction with Sauchiebank head up the recently opened Roseburn Union Canal path, again this is signed.

Follow this up and over the railway and then a minute later over Dalry Road. Walk past the newly redeveloped Dalry Community Park and at the far end cross the Western Approach Road at the lights. Head up towards Fountainbridge library. Cross Dundee Street and turn left, walk one block then turn right up Gibson Terrace and follow that the short distance to the Union Canal. If you don't want to cross the Western Approach Road at the lights then take the lower path, down to your left, at the far end of Dalry Community Park. This will take you down to the Telfer subway. Turn right and walk through the subway, below the Western Approach Road, then follow the path and/or steps up to Dundee Street and Fountainbridge library.

Turn left along the canal and walk the few minutes from here to the swing bridge at Leamington where you can pick up the Walkhighlands notes at Stage 8.
Downside to this route is you miss out on Corstorphine Hill. If you want to include Corstorphine Hill you can still do that and pick up the above route at Roseburn. When you drop down from Corstorphine Hill to Corstorphine Road (the A8) turn left and follow that the 15-20 minutes or so to Roseburn, passing by Murrayfield Stadium en route. The road crosses over the Water of Leith at Roseburn and about 100 metres after that passes below a bridge. Turn left, immediately after passing below the bridge, and head a few metres up Wester Coates Terrace before turning left up a path that brings you onto the Roseburn Path. Again, this is all signed. Turn left along the Roseburn Path (or turn right if you want to see the views from the bridge down to the Water of Leith) and follow it for a couple of minutes to its end where you turn right, as described above, and drop down to Russell Road.
If you want an indication of time it took me about 90 minutes to go from the junction of Whitehouse Road and Barnton Avenue West to the canal at the top of Gibson Terrace.