Finally, after desoldering both CIA chips I noticed than one via below U8 had completely disappeared. Since it was gone completely I missed it the last time I desoldered U8. The other vias in the area looked 100%, so it seems a little weird how this one could have gone like that.
I fixed the connection, soldered in both CIA chips, and so far it works, so hopefully another Amiga has been saved from eternal sleep.
It boots perfectly from floppy or HDD, and since I haven't been able to get my ACA620 completely stable in my other A600, I can now test it in this one to see if I can get it to work better.
Edit: I also found another broken via right next to the RGB port (see picture), although I'm don't think it would cause it not to boot.