I thought the "via Wycombe" ticket was what it says, not a Chiltern only ticket. Doesn't the ticket say "Birmingham stations" rather than Snow Hill or Moor Street? You might even want to go via New Street to avoid a walk if you were splitting a ticket at Birmingham.
I am not going to get into another discussion about whether a discount can override the interavailability of a ticket, as we have had plenty of discussions on this subject and never managed to reach a consensus.
For the record I believe that Condition 10 should not be undermined by the specific conditions of a discount not explicitly printed on the ticket, however I am of the view that as things currently stand, there are good arguments to say that they can (one of which I note Arctic Troll had already covered).
From a practical point of view, doing so in this particular case would simply be asking for trouble and there is likely to be very little benefit (If XC were empty they'd be picked up by the guard and end up in an argument. If XC were busy why change from Chiltern?), so I advise against it. There is a time and place for a challenge, and this is not it imo.
