Before you try to put the barrel on, use a straightened piece of coat hanger wire to drive the button out from the inside of the barrel. It will resist, but it will come if you push firmly enough. As an alternative, if you have a tool for removing Vacumatic fillers, the threading of the metal collar is the same as on the Vac, and you can remove the entire button assembly (two pieces).
Assemble the barrel to the section, then slip the pressure bar down the side until it stops firmly, being careful not to catch (and push on) the end of the sac. Then you can reinstall the button. Do be careful to insert the pressure bar right-side in/out. Here is a cross-section of a button filler, showing the correct orientation of the pressure bar: