hi everybody,
many times (99%, I feel) we come here with a problem, post a few questions, get valuable info, and then don't feed back everybody with the outcome. So this is my attempt to improve that.
I took the bike to my very trusted dealer, who has a good mechanic, but he wasn't there. So the "2nd in command" bled the brakes. This is what I mentioned on the title of this thread. I don't know what he did, but that day I drove home and the behaviour was more consistent, but the next day it was back to square one: first lever pull would take quite a lot of dead stroke for the pads to start biting. Letting go and pulling again rapidly would move the biting point to where it used to be, with no dead stroke on the lever. Waiting 5 seconds and trying again was enough to bring back the "dead stroke".
Discs are at 4.65 mm, pads are rather new.
So I took the bike again this week (I had to get other stuff done) and this time the good mechanic was there, so he power bled the brakes twice and the master cylinder. He also pulled the callipers out and cleaned and moved the pistons in and out to let the sealings slide and reposition correctly. He also added a tiny amount of brake fluid.
Result: bike brakes like new!

I didn't have the chance to do hard braking because of traffic, but I'm more than satisfied now, and he barely charged me 20 minutes of his time.