Jura E8 - lower piston head is stuck

I'm dismantling my Jura Capressa E8. I've removed and mostly dismantled the brew group, but I'm having trouble removing the lower piston head. Videos I've seen show people just pressing it out from beneath, but mine seems to be stick in home position (that is, at the bottom of the housing). The six white gears/cogs around the shaft don't seem to move, and I can't push it up. Any suggestions how to fix this? If I remove the compressor cup, it would enable me to access the white gears, but I'm not sure I can remove that with the piston head still in place.

Put the cylinder with the opening down on a surface and then press from above on the gearbox. It may be that he runs hard. But so you get him out. It may be that you have to press hard.