Have you tried both the National Rail and the London Underground TVMs at Tottenham Hale?
Not saying the latter will sell that ticket, necessarily, but it wouldn't surprise me either way.
Thank-you for the homework assignment.
I arrived this morning in off-peak and tried both sets of machines in Tottenham.
National Rail machines: First result was realising that I while I couldn't change the origin station on start, once I had got the machine to quote for a ticket so I could on the second lap select LU123-LNY. This came up as 9.25 as expected. Great. I have a way to buy tickets without online or kiosk.
The London Underground machine can't change origin, but showed 9.10 as the Gold discounted fare from TOM to LNY, discounted from 13.90.
I can't make this make sense as a fare. Does LU use a different percentage discount to National Rail for the Gold Card? It is too high to be the "restricted to Ealing Common" fare that I accidentally bought this morning. It is not high enough to be the contactless fare (9.40, no Gold discount) or the standard paper ticket (13.90). I'm afraid I chickened out of making the purchase but may try this tomorrow...unless I opt for a cheeky offpeak return.