Not your personal area of interest, but might be worth reminding about restrictions on non-folding bikes. I presume the restrictions into Paddington at peak times also apply from Melksham.
A slight red herring. Have been told at Reading that there is no restriction on using off peak tickets coming back from Waterloo. Is this only for Reading and Windsor lines and not applicable to Wessex lines?
Cycle reservations required for none-folding bikes on all connections to / from London, but no peak bans. I stopped short of dogs, cycles, luggage and wheelchairs in writing though perhaps I should add them.
Not sure on restrictions from Waterloo as far as Reading, but Reading onwards does have peak restrictions on Melksham tickets - it's once the trains get to Didcot that they suddenly become super-off-peak ...