Presumably some simple limitations could be made to allow the abolition of peak restrictions, such as the railcard not being valid before 8am (That meaning anywhere on the network, clearly allows those commuters within an hour of London to use a train which leaves at 08:00 and arrives in London in time for their work). Removing the evening peak would mean you do not have any restrictions on leisure travellers.
In terms of those who might be enticed to the rail network I think that keeping advance tickets would be no bad thing. Whether the railcard then allows discount on advance is open to discussion.
Aside from the specific train restrictions of advance, and the fact the railcard cannot be used before 8am, I would keep the rest of the tickets as a simple point-to-point price with London restrictions meaning routes where via London is not the quickest become two parts.
That then made me wonder about Wigan (either) to Warrington (either) since that can be done direct (if North Western to Bank Quay) or via Manchester. Should that ticket be valid via Manchester or should it be insisted that a direct ticket exists between North Western and Bank Quay so you cannot use Wallgate to go to Central via Manchester? There are many such potential anomalies around the network.