To the best of my knowledge you can change Avios bookings up to 24 hours before departure even when the first legs have been flown, but they do become non refundable once you get to 24 hours before the first flight departure.

I'd call back and see what the agent can do. If there's no D class then that a non-starter, so look at A class for First as well. It'll get messy to FTV this with what is effectively half a joker so a decent agent should be able to find you a workaround. But do the work for them and make sure you're asking for seats on a flight that has 'jokerable' fare buckets available.