I haven't been following this thread, so I apologise if this has been covered already.
Early this month I booked a return trip from Lancaster to London for 2 using Avanti.
Initially, it appeared that I couldn't buy tickets without reserving seats, although I couldn't see this stated anywhere. I got a message that no reserved seats were available for part of the outward or return journey, but no clue to which train(s) were affected. I tried a few different trains, but no change.
I tried again later and managed to book tickets without reservations.
I went to Penrith to collect the tickets but the computer said no, without giving a reason. (Do I have to go to the same station as on the ticket?)
Fortunately the ticket office cancelled the booking and sold me new tickets without reservations. The refund for the original tickets came through within a few days, but I didn't receive any message from Avanti.
I guess I'll try Trainsplit next time. It's usually not convenient to visit the station.
Can you buy any other TOC tickets from the Northern ticket machines?