I've no idea why National Rail are showing some options via Stroud as valid. Routeing Guide says no. As do booking engines when you actually try to book a ticket specifying 'via Stroud'.
However, the route should be valid. I see no logical reason why the Routeing Guide disallows it. There is no doubling back, no fares extraction issues, and circulating via Swindon and Cheltenham with cross/same platform interchanges is just as passenger friendly as going via Bristol or Didcot/Oxford.
You could ask the fare setter (CrossCountry) if they'd ask the Rail Delivery Group to amend the Routeing Guide. I can't see any unintended consequences by allowing travel via Stroud but
XC▸ and
RDG‡ may find some. Or, more likely just put the request in the 'can't be bothered' pile.
Instead, if this is actually a fares request rather than a thought experiment, then I'd suggest the following:
Split your tickets at Stroud.
Trowbridge - Stroud, Anytime Return £32.70
Stroud - Birmingham Stns, Anytime Return £61.10
Total: £93.80
Or, alternatively, if you can live with travelling via Bristol instead and really want to stick it to the man then you can use the following tickets:
Trowbridge - Bath Spa, Anytime Day Single £6.40
Chippenham - Bromsgrove, Anytime Day Single £35.90
Bromsgrove - Chippenham, Off Peak Day Single (provided return is after 0829) £21.10
Bath Spa - Trowbridge, Anytime Day Single £6.40
Total £69.80
Those middle two tickets allow travel via Birmingham New Street thanks to the following easement:
700147
Customers travelling via Yate to Bromsgrove in possession of tickets routed "Any Permitted" may double back via Birmingham New Street. This easement applies in both directions.Starting or ending short, as well as break of journey, are allowed on those tickets. The easement routes you via Birmingham New Street. One just forgets to double back.