What is needed next is a third reversible line on the Up side between Reading West and Southcote Junction with or without a possible flyover at the latter
That's quite heavy engineering through a built up area, isn't it? Would an alternative capacity increase for freight to Westbury from Reading be to provide a second track from Thingley Junction to Bradford Junction, where there's already a trackbed as that line was double until 1967 (actually double broad gauge in the 1800s!)
For just a few trains maybe ... but (if you believe the Western Route Study - which is not compulsory) the twin track from Swindon to Thingley overloads before Southcote Junction. Plus, of course, those trains don't want to go just between Reading and Westbury. If they are taking aggregate from the Mendips to London, they would need to go through Didcot East which also overloads early. By 2019 its grade separation will likely be at
GRIP▸ 3, at most. If they are taking containers of goodies from Southampton to past Birmingham, they have to get across to Westbury, which is a longer route (though part is identified for possible electrification in
CP6▸ as a diversion for the Electric Spine up to Basingstoke).
The Route Study considers the third track from Oxford Road to Southcote, along with grade separation at Southcote (option C4). The third track is a bit more expensive (^35M - ^75M), and includes relocating Reading West station - where to, I wonder. That north part of the formation is between rather short back gardens, so I suspect the idea is to use the width occupied by the platforms so as to avoid any land take.
Part of the analysis of the two parts of option C4 says this (p137):
Either choice would increase capacity and reduce performance risks along the Route Section. However it is anticipated that the delivery of these choices would still be insufficient to deliver the full 2043 ITSS without compromise to the journey time improvements anticipated in 2019 due to key constrained areas on other Route Sections such as London Paddington to Reading where capacity utilisation is high. The implementation of both choices together is expected to mitigate this with the combined intervention allowing efficiencies to be realised which would reduce the overall cost.
I think that says that either the grade separation or the third track alone would not deliver the hoped-for reliable journey time improvements as the line from London to Reading is so heavily loaded. But doing both would mitigate this. How? Any timing improvements over this short section can't possibly be enough to cancel out the kind of delays that could be produced by a small initial disruption on a fully-loaded 20-minute-plus run out to Reading.
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