Just got off the phone to book an open jaw return from South America. The midnight call to the freephone silver number in the US worked ok and they reserved the seat.
Looking on SeatSpy at 00:25 there was no J availability any more so it really was the only way to go. I rang up at 23:45. It took a couple of minutes to get through the menus, but the phone was answered relatively quickly (low demand at this time of year) and the lovely guy on the other end of the phone was happy to sit around for a few minutes.

Interestingly, looking at my account, they refunded all the charges for the first booking and then recharged me the avios and tax for the complete booking (so it looks like a refund and new booking in the app even though it is just an 'adjustment').