In the years (and years) I've been flying and redeeming points with BA, I've found the best way to use the points - and in your case, upgrades - is to book during low season and shoulder season. I used Avios to fly First Class on BA to Washington DC... in January. Back when EI J was a sweet spot at 25,000 Avios each way on BA to BOS, I did that in winter too. Availability is always higher for frequent flyers sort of during the October to April period in the Northern Hemisphere because it's not the summer high season where airlines can sell most of the seats for cash.

The other thing I've always done is to be creative. Have you tried places like DEN or MSP or BDL or CLE or IAD? What I've done in the past is used my points to another city where there was availability, and then just bought a cheap internal flight to get to the place I actually want to go. For example, I found availability once to MCO when I wanted to go to MIA, so I booked MCO with points and booked AA with cash MCO-MIA. Yes, it's a connection, but the saving using points on the transatlantic was way more than the extra cost of a connecting flight.

I'd certainly be doing something like that over losing the upgrades.