I think the service between Bedwyn and Pewsey is so awful that it needs an extra service...

So I reckon this could be done:

1K44 1118 London Paddington - Bedwyn extended to Pewsey, timings modified as follows:
as now to Hungerford (1222), Bedwyn (1228), Pewsey (1234). Run ECS to Woodborough and reverse.

and therefore 1K49 1307 Bedwyn - London Paddington could look a bit like:
Pewsey (1302), Bedwyn (1307)

If there was enough time, that could probably be extended to Westbury if the gap of services was increased.

Seeing as the crew stay on the train into Bedwyn siding, a driver cannot take a PNB 'on train' so there is no break, the crew swap takes place at London Paddington.

Traffic levels probably wouldn't be fantastic - but the key reason why I suggested it would be to act as a glorified ECS service (like 2R99 Southampton Central - Filton Abbey Wood) to retain route knowledge to Woodborough in the event of a failure at Bedwyn stopping access to the siding. Although Swindon would probably turn back at Newbury in that eventuality.

I just had a quick look in my 2005 NRT, looks like there was an 0818 London - Exeter St Davids which called, as was a 1218 London - Exeter...