Pity that the setting up of the proposed Parry People Mover service from Alton to Medstead has been such a palaver - otherwise I'd be suggesting running a PPM up and down from Yeovil Pen Mill to Yeovil Junction to allow passengers from the LSWR line access to the town, and also to provide an interchange between the LSWR and GWR lines -then there would be no need to reinstate chords and the like and waste time by inserting an additional call at Yeovil Junction.
As for the "Quicker by GWR route argument", it's arguable that comparing journey times from Paddington and Waterloo are necessarily comparing like with like. It depends where your starting point in London is and then you have to factor in the travelling time from there to either Waterloo or Paddington. On that basis, the journey time via Waterloo would always be quicker from the City and WC area.
As for Lyme Regis branch - has anybody ever mooted the suggestion of a narrow gauge line which would then serve the dual propose of transporting people to the town and being a tourist attraction in its own right? Easier and cheaper to construct, and less land needed for a station site at the far end. I don't think that everybody would be put off using the train if there was a frequent park and ride service - when I go to Lyme in the summer I use the Park and Ride car park on the A3052 which is just over a mile from the Cobb (where the minibus drops you off) and approx 150m above sea level, so further from the Cobb than the old station was from the town centre.