It is valid via Reading only if travelling between Taunton and Reading via Newbury (by maps MW and WE of the routeing guide).
I'm pretty sure this is incorrect and it is valid via both Bristol and Newbury
Taunton is a routeing point
Burton on Trent is a member of Derby, Nottingham and Tamworth routeing points.
Taunton to Burton on Trent (SVR- £65.20)
Taunton to Derby (SVR- £71.10) Fails fare check rule
Taunton to Nottingham (SVR £71.10) Fails fare check rule
Taunton to Tamworth (SVR £63.20) Passes fare check rule
So the valid routes between Taunton and Tamworth are
CE, CE+SW, MW+SW, MW+WE, MW+WR, SW+MW+TL, TL+MW+WE, TL+MW+WR
Using maps MW+SW
Starting on map SW you can travel Taunton to Bristol (via Weston Super Mre also if you wish) and then Bristol to Swindon either via Parkway or Bath & Chippenham and finally then Swindon to Reading via Didcot.
Then once at Reading you can travel back via Didcot, Oxford Banbury, Coventry (or via Solihull if you wish) and then Birmingham to Tamworth.
This obviously does raise a few issues using the routeing guide, firstly using the maps in the order SW+MW instead of how they are written as MW+SW but on consulting the examples section the following is stated
If the route code has several maps, route tracing must observe the following rules:
1. Tracing must start at one of the ends of the route code.
2. All maps must be used.
3. Maps must be used in strict sequence,
first to last or last to first, according to the end of the route code where reading began.
4. Tracing may move from map to map only at a point where the two maps touch.
5. Once route tracing has left a map it cannot return to it.
6. Journeys may not double back except between stations which are members of a routeing point group for interchange or unless an easement permits it.
Also doubling back between Didcot and Reading, this is covered by an easment.
000082 Journeys via Swindon and Didcot or via Swindon to Didcot and routed Not London may double back between Reading and Didcot. This easements applies in both directions..
So the OP can legally travel via Reading, either travelling on a service via Bristol or Newbury to reach Reading, on any train after 0500.