I mounted up the brifters on an old handlebar and found an old shifter cable in the bin, so my test setup was fine.
With copious WD-40 and a heat gun, I got the LH shifter working, though still a little crunchier than I'd like.

The RH is still problematic, despite coming close to overheating it and melting things. I put PB Blaster in it to sit overnight.