On the Bedwyn subject, I think the main problem there is the bizarre fact that you can't get to Pewsey without going via Hungerford or Newbury. It's not the only case (try going to Chathill and asking for a return to Berwick) but they are only nine miles apart.
Assuming they electrify to Newbury, you could run an hourly Reading-Exeter stopper as a collector, but that would not actually go to London. As a result, Kintbury, Hungerford and Bedwyn would lose their London service. It might end up incorporating the Reading-Basingstoke service, unless there were diagramming problems.
Basingstoke-Bramely-Mortimer-Reading West-Reading General-Theale-Midgeham-Newbury-Kintbury-Hungerford-Bedwyn-Perswy-Westbury-Frome-Bruton-Castle Cary-Somerton (ideally)-Langport (ideally)-Taunton-Wellington (ideally)-Tiverton Parkway-Cullompton (ideally)-Exeter St David's
This would be a very long, slow run, and might require a few waits in loops to allow expresses to pass. It's also possible to split it at Westbury, maybe with the eastern portion diverting to Warminster and the western portion to Swindon via Melksham. The reopenings are probably impossible, but this is the land of wishful thinking :?
However, it's been a while since I went to school (near Frome) so I don't know if things have changed much. Maybe the idea of a slow train cantering along the B&H is just plain fantasy, especially as I know the signal headways are a bit long down there.