if you can be up very early, the 0557 is definitely valid. If you want a lie-in, the 1109 is definitely valid and I reckon the 1102 is valid too.
In between those times, the interpretation is difficult, and I wouldn't expect a barrier person to understand it, and wouldn't want an argument with them, so would buy a ticket to Reading West (£1.10) to avoid that 'discussion'. I would then strongly advise against boarding a train that originated at any place where the restriction 'XC' applies, in other words, if in a rush I would get a fast train that originated somewhere like Oxford.
However it would be safer to get a train to Waterloo, as this is a really complicated subject and you just don't know how the guard is going to interpret it, if a check is made. If you're travelling round London, I'd get a Travelcard in advance and use that to exit the barriers at Waterloo to avoid a 'discussion' with barrier staff who do not understand the restriction.
There are many barrier staff who seem to think there are blanket peak times, they think that TOCs have the right to decide to bar all off peak tickets from anywhere to anywhere at certain times, they do not understand that tickets have validity codes. It's not only beyond their training, but for some of them, given the pay is quite low, it may even be beyond their comprehension (this isn't an insult, it's the honest truth; you can't expect someone on a low wage to understand the complexities of our ticketing system, and neither can customers be expected to understand it!)
My opinion is that a valid itinerary would be 0523 Swindon - Reading, breakfast in Reading, then any train Reading - Waterloo, and any train forward to Eastbourne.
I believe that if going to Paddington, one interpretation would be that any train could be used after a break at Reading, another interpretation would be that any train other than the barred trains would be valid, but some staff may 'invent' an interpretation such as all HSTs are invalid (like what happens in the evening peak) or that all trains are barred from Reading to London until a Reading to London Off Peak ticket is valid, or goodness knows what other interpretations they may have!
In 2007 I did a valid BOJ at Slough, but the staff at Slough decided it wasn't valid for BOJ (they were wrong), I had to argue with them for around 30 minutes and they defaced my ticket. I did not want to miss my train in the morning so I bought a ticket to somewhere like Windsor or wherever to avoid that discussion. I see nothing wrong with buying a ticket that you will not use, in order to avoid badly trained, incorrect, and sometimes downright rude, barrier staff who do not know what they are talking about. The guards are who matter, and they were all fine with my, perfectly valid, ticket.
While I am not saying that all FGW barrier staff are like that, my experiences of FGW barrier staff and RPIs is such that my default position is I do not trust them to accept that a valid ticket is valid if the validity is complicated, and therefore I will try to minimise conflict with them. But when that conflict does occur, I ensure I win.
