Mkay...

Finally 'solved' the issue: The problem is the Aten US 424 USB switch.

I needed to disconnect it completely from my PowerMac G4 DP, even if there are no devices connected to the switch! If it is connected it interferes with the MorphOS installation in strange way (it seems), always leading to this freezing issues during install sooner or later. Actually does not matter if I install on the SSD or the HDD hanging on the SiL 3112 SATA controller or to a HDD connected to internal IDE - I was not able to finish installation.

As soon as the Aten US 424 is not connected from the beginning, all these problems disappeared. Installation on the SSD works a-ok, running the installed MorphOS works a-ok. That's the good part.

The bad part is I really miss using the Aten US 424. It's so convenient to switch between different machines. Also the switch works fine with my other machines and also on Gentoo/Adelie/Void-Linux on this very PowerMac.

Is there a chance this situation improves with future MorphOS versions? Are there any 'known good' USB switches cooperating well with MorphOS?