Thanks for your help, I was able (I think) to make progress.
The issue was the glass, I dropped it: it's less shiny but the result is really
better. My guess is that the IR doesn't go through that glass so one have to
wait until the glass get hot.
Did some experiments at different bottom temperatures, I can now reach 120°C
with 330°C at the bottom and 160°C with the bottom at 380°C, the only issue is
that the bottom controller is far too slow on the last degres to ramp up, it can
take minutes to get the last 20-15ish degres, and I guess sadly that the PID is
not configurable. I finally faked it, by putting 20°C above and reducing the
temperature near the desired temperature at the top. With that and the
120 -> 180 -> 225 steps I finally was able to lift the CELL in less than
12 min or so.. The internal TC was at 210°C while the external 225°C, so I'll
probably try to find a replacement. Finally I messed up the capacitors behind
the CPU with that suction pen

.