I know next to nothing regarding how the barrel is mated to the breech. I once tried to switch out a barrel on an older Chinese springer. In that case a cross pin was used to secure the barrel to the breech. It was very hard to see the pin as it blended almost invisibly. My attempt was not a success, even after driving out that pin, which was hard to do, I could not get the barrel to budge. I didn't have a press of any kind, and I'm sure it would have made all the difference. I think using a press will give you the results you seek, just make sure there is not a cross pin.
... you can search in Youtube "Restauración de una carabina Cometa V" and you can see a complete video of restoration of a cometa V model .Cometa 5 or Cometa V it is the same model.
I believe it's Jim Maccari's (sp) site.