That does sound more feasible but it would cause a dramatic reduction with linespeed as the current lines have a 70mph restriction compared to the 25 on the current chord which is a similar radius to the proposed one. Also if you wanted to keep the current capacity you would have to improve slateford junction which could be awkward with the station location, at the end of the day i can't see a day where this idea would work as i can't see it freeing up that much capacity and if haymarket is that full up you would need a long term solution to the capacity problems such as something like the proposed glasgow to edinburgh high speed which could use a new alignment entirely
The idea here is that although the existing route is reasonably high speed, there is little way to improve capacity on it because the junction is only metres before the Haymarket platforms. Even though reconfiguring it would reduce linespeeds, it would benefit much more from being able to have a much more sophisticated junction. There's no point having a 70mph route if most trains would have to slow to a crawl or stop waiting for the junction to clear.
If the connection between the two lines were modified like this then the existing route would be abandoned completely and the main line would swerve from Slateford up to Murrayfield. Demolishing some buildings to increase the curve radius would be not unreasonable by the time this intervention needs to be done as every other capacity enhancement possible will require it. I imagine that the then-abandoned railway route could be retained for a future Edinburgh Trams line to the south west of Edinburgh.
One of the things which I have found most interesting about seeing the planning portal plans for the new platforms is that it also makes it clear that it would be possible to fit in a reasonably-sized HS2 terminus at Waverley, effectively taking over the entire set of southern through platforms. The length is already there, all that would be needed would be for them to be rebuilt to be completely standardised (i.e. perfectly straight or curved, no sidings) and at UIC gauge. Such a reconstruction could even be done piecemeal while the station is in use, with each reconstructed platform given back to classic rail services in the meantime using a temporary raised surface. The most efficient way to increase capacity for high speed services in the long term is to build a tunnel from Waverley out to join any high speed route to Glasgow and the south. That would allow extra HS services and relief of passengers to Glasgow but I can't see it really freeing up too many paths, as those currently used for these services would still be running but wouldn't be carrying end-to-end passengers. There would still be around the same number of ICEC services going eastwards but calling at more intermediate stations and the 4/6tph to Queen Street would now be all-stops affairs, but those changes only really affect pathing well outside of Edinburgh.
Over on SSC there's been a bit of discussion about single-bore metro tunnels, which is when you use a single very large tunnel for both directions of a metro line which is also constantly large enough for the platforms. Tunnelling with a TBM is cheap now, it's the stations which are expensive. Any east-west tunnel under Edinburgh wouldn't be that long, so the option of using a larger TBM which would be large enough to carve out a single track platform tunnel is an interesting one. Originally my thoughts for building an east-west tunnel involved using the southern surface platforms at Haymarket and then rebuilding the tunnel east of there to head downwards into a new tunnelled station underneath Waverley itself. Using the large TBM technique it could be feasible to have Haymarket as an underground station as well, which would also help with construction staging and rail capacity. What I'm thinking now is that the lines past Murrayfield could be changed to be paired by direction, after adding a new flyover/under where the E&G and Fife lines split. At Murrayfield, the new South Suburban/Slateford line would then have an easier time connecting to both as each track direction could join in between the two mainline tracks of that same direction. Just after that line joins in the new tunnelled tracks could split away from the middle as well and then run down into the new underground station at Haymarket, leaving the surface tracks for longer-distance services. Since the HS2 works would remove the southern side of Waverley from the classic network, there would be no need for four tracks beyond Haymarket. Instead each running line would have two platforms, so that platform dwell times would no longer restrict capacity.