You can get Advances that include travel on the Cotswold Line to certain destinations following a change in London. Norwich is one such destination.
However, SickyNicky said he had an Advance to Paddington on the 0642 from Hereford. Could be he had an Advance to a destination beyond London, but that isn't clear. Neither is the response...
... which didn't really answer the query.
I can't find any Advances ending at Paddington that allow travel on the Cotswold Line.
Just so. And they aren't going to offer them when you can use a Network Card all the way out to Worcester and the Cotswold Line Railcard makes many local journeys at stations between Oxford and Worcester a bargain off-peak.
If you want to spend a lot of time faffing around with splits at Oxford, using OXF-PAD advances for the eastern leg and a Cotswold Line card west of Oxford, you can save a couple of quid here and there but is it worth the hassle?
Especially when there is an easement allowing use of Network Card fares on the 08.26 from Worcester, plus the ability to use off-peak returns on the 06.42 departure from Hereford at stations west of Oxford and go home on an off-peak return using any afternoon peak service from London - all of £54 from Hereford to London and back.
Travelling Chef breakfasts will certainly be missed on the Herefords - it's not unusual for them to run out of ingredients well before Oxford on busy days.