Only going as far as Bristol makes things easier, as a Swindon-Liverpool journey is valid (on maps BW+BV) with one change in Birmingham.
The double back to Reading is absolutely fine with a "not via London" ticket. Easement 82 says as much, and the reason behind it (that Crosscountry doesn't stop between Oxford and Reading) is as sound as ever. For confirmation, nre.co.uk is happy to show that route as being valid (
link*).
From what I can see, going down via London will be quicker, but going via Reading cheaper. The "via London" excess should cost £14.85 or £14.90 each with a railcard (I don't know how exactly the rounding works here). If you go via Reading, you can use contactless for £5.20 each off peak.
For the journey to Bristol, your return leg would cover you from Swindon (maps BW+BV via Bath, or SB+PM+NO via Bristol Parkway). Going to Swindon, a £14.30 (with railcard) super off peak single to Swindon (restriction
YU) may be suitable.
Sorry, I should have made the situation a bit clearer. The outward ticket will only have one day's validity printed on it, so you are likely to be asked questions if you use it after then. The return has a month's, so you aren't.
To minimise the risk of hassle, I'd take an itinerary with you (either printed or on a phone) in case someone asks. A Liverpool-Swindon ticket is valid via Bristol Temple Meads but a Birmingham-Swindon one isn't, so I wouldn't rely on the barrier staff knowing.
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