Not entirely sure why you want to focus on enhancing the Chiltern mainline from Birmingham when that’s exactly what the big HS2 plans are for - and the only reason OOC station is being built for in the first place?
Chiltern goes to more places than just Birmingham...
Any enhancements towards Birmingham via Chiltern are just duplicating capacity.
Chiltern goes to more places than just Birmingham...
Seriously, OOC platforms are for adding terminating capacity to allow more local/regional service between London and Bucks/Oxon. Diverting a couple of trains an hour to OOC (and adding a couple more from OOC) would allow those paths to be used for the 'Chiltern Metro' enhancements, or more trains via Amersham, or increased service through Wycombe to Aylesbury, Banbury, Oxford, etc, or a mix.
Surely it would be better to enhance a potential line towards the SWML if we are going really crayonista..
Chiltern to OOC is merely build some platforms, and rebuild (in a slightly different place) some tracks closed for HS2 construction. It's cheap as chips (as far as rail schemes can be), and barely registers on the crayonista scale - a long way from "really crayonista".
It is priced at £210-£360m, the majority of which is upgrading the existing line to 80mph double track. £50-£100m for the platforms and track connection near OOC.