That restriction text is a little dated now. The railcard easement on Virgin services now applies only to SVS/SVH/SVR flows priced by Virgin
AND for which the entire journey is on a Virgin train. The easement now reads:
Holders of Off-Peak ticket types SVS/SVR, which are discounted using 16-25, Senior, Disabled Persons, HM Forces and Family & Friends Railcards and New Deal Photocards, can travel on Virgin Train services at any time, provided that all travel is on Virgin Trains services only. (This easement is not permitted for travel between Milton Keynes Central and London Euston).
My emphasis in
boldAllegedly because other operators were not happy having Off Peak passengers on their Peak services. There were incidences of passengers on connecting services being incorrectly chinged for excesses or threatened with prosecution for travelling with an invalid ticket.
In some cases you'll need split ticketing to yield savings when the journey is not wholly with Virgin. Virgin themselves admitted as much in an information update sent to industry partners. That info was briefly on line back in December but has now gone. It said:
There has been some confusion on the use of railcards on Virgin Trains Services.
To clarify, customers purchasing off peak ticket types SVS/SVR, which are discounted using 16-25, Senior, Disabled Persons, HM Forces and Family & Friends Railcard, can travel on Virgin Trains services at any time.
An example of this, a customer travelling Euston to Manchester with a railcard can travel anytime with SVS/SVR.
However, if a customer starts their journey at Euston travelling to Bolton and is travelling during the peak time, an off peak ticket will not be offered using any railcard.
Separate tickets would need to be purchased between Euston-Manchester and Manchester - Bolton if a customer wants to take advantage of travelling during the peak with SVS/SVR and a valid railcard.
If a customer travels Blackpool- Euston leaving 07:00, an off peak ticket will not be offered in any retailing systems.
A separate ticket would need to be purchased between Blackpool and Preston.
This easement is not permitted for travel between Milton Keynes Central and London Euston.
Regarding catching a train from Taplow at 0829 on a Taplow to Stoke-on-Trent SVR. That is allowed thanks to something called the 'Network Area Easement':
Off-Peak tickets for journeys starting within the Network Area to destinations outside the Network Area with travel via London are valid by any train to London, to connect with trains from London.
Off-Peak tickets for journeys starting outside the Network Area for travel via London use restrictions from the origin station to London and return. Unless shown otherwise, they are unrestricted between London and the destination station, and return.
The Network Area refers broadly to the former Network SouthEast area, which Taplow is in. As shown on this current Network Area map:
http://www.railcard.co.uk/clientfiles/File/map.pdf
Finally you'll have more than 1 minute to get from Euston Square to your train from Euston. The journey planner you've used has applied the 43 minutes
'Cross London Transfer Time' between Paddington an Euston. That 43 minutes from 0916-0959 is not referencing the actual tube timetable, you'll find, all things being equal, that 43 minutes is plenty of a time for that transfer.