Many, many thanks for the the very detailed reply and suggestions. Good to know in advance in particular about the possibility of the IB app giving a your first flight is operated etc." error message. I had forgotten also that the BA app also shows ticket numbers - those all look fine (they are there for every leg of the journey, including the MAD-GRX leg).

Thankfully the MAD-GRX flight is the 22:00 flight - an Iberia service rather than Air Nostrum. I've booked some assistance anyway (through BA - confirmed by calling with IB) as after a long day of travelling I think I may still need it.

As it happens, on-line check-in is now open for the trip - and with unsatisfying irony I was able to check-in and download the boarding passes for the IB flight without problems, but still can't check-in for the BA flights...! I'll get on the phone later to double check about that - but could just be due to the need for a visa check for my partner.