Interesting discussion on the test ROM, sounds like something I will need to investigate.
For my A600, my colleague had some time to look at it and to try some reflowing. He said one CIA had perfect connections (as far as he could tell under the microscope) and so he left that one alone. The other CIA did have some bad/cracked connections and so he reflowed what he could (one side of the chip is very close to another component and not easy to get to). Unfortunately this does not seem to have had any effect on my serial problem. I think I may now also now have a floppy drive problem but I am still checking that I did not make a mistake reconnecting everything.
While he was looking at the board my colleague also noticed some scorch marks especially under U-29 (whatever that component is). I assume that is not normal
This has gotten well beyond anything I or my colleague is able to do so I am now trying to find someone offering Amiga repair services. There seems to be someone on English Amiga Board that is not too far from me so I will reach out to them and see if it is something they will take a look at.
Hopefully it can be repaired otherwise my Amiga journey might be over for now.
Thanks for the help and information.