It's been quite a day.
Tried the Eezibleed with an extra rubber washer in the cap and the reservoir's no longer overflowing when I shut off the nipples, and the level is staying the same. Had a look at the nearside rear caliper though, and it's leaking from the nipple. Turns out the threads are shot and even though the nipple was screwed in tight, there was no way it was going to hold pressure.
Ordered a replacement caliper from Euros and went to pick it up. Turns out it was an offside rear in a nearside rear box, and they can't get a replacement in until tomorrow.
Sometimes you just want to cry.
I've sprayed PlusGas into the threads and I'm going to crack the bolts on the caliper mounts so I can be as quick as possible changing things over when I get the right (or should I say, left) caliper tomorrow, but I suppose the takeaway from all this has been that to get the feel in the brakes that I was getting - which is pretty firm - once I replace the caliper, things should all come together pretty well.
Someone once told me that the Leon calipers are made of cheese, and I never really got what they were saying. Now I do.