My pressure bleeder finally arrived - it's a Schwaben Compact bleeder.

I spent a couple of hours on it, had some issues with the bleeder as first it wouldn't seal properly around the reservoir (which I resolved with some teflon thread tape) and then it also seems to leak around the fitting which has the gauge on it (but this is a problem for another day).

Anyway I have made significant progress now. A ton of air came out of the rear right and front left calipers, it was very very frothy. I bled probably 2 liters of fluid through the system.

The pedal is a LOT harder but still not quite where it was before all this mess started. Obviously I need to bleed it a bit more which I will do later this week and report back. But it's looking good thus far.