Hmm... the usual rule is that if both trains of a two leg journey using an Advance Purchase ticket are reservable then you must stick to the booked trains.
In the case of a journey from Taunton <-> Salisbury via Westbury both trains will almost always be ones that offer reservations, so one should, by the letter of the law, stick to ones itinerary.
There's nothing stopping you asking for discretion to travel earlier/later, but this should be done before boarding the first train, and clear unambiguous authority (i.e. an endorsed ticket or station stamped note) should be obtained. Don't rely on "the man at the station said it would be OK".
I really would recommend using the available assistance. It's free and if there are problems then it'll smooth the way for alternative arrangements to be made.
An alternative is use
FGW▸ 's step-by-step 'text only' booking engine where you can specifically request an extended interchange time and have this included on a booked itinerary with a through ticket. This though may reduce the options for the cheaper Advance Purchase tickets.
http://tickets.firstgreatwestern.co.uk/gw/en/JourneyPlanning/Wizard/JourneyDate.aspxAnother alternative is to book the legs separately with the extended interchange time you want, but in this instance that will likely be more expensive than a through ticket.
With details of the actual journey, date, times (out and return), number travelling, railcards, I can maybe advise further.