Well, I was right in that some config file was wrong. The migration procedure is incomplete it seems.
I had followed the migration guide completely, therefore all passwords were updated as stated for localconfig.xml.
I had found some other posts somewhere that after migration, it was suggested to run:
but I did this and it didn't solve the problem, I still had the error with zmldapanon not working and not allowing me to connect. Therefore, what solved the problem was to do this:
which would effectively detect my Zimbra install, and run an upgrade. Of course, I was just running the 6.0.8 install again upgrading 6.0.8 to 6.0.8 (the same version).
After this had finished, when I ran zmldapanon -e it worked fine and now it seems whatever config file was missing a password or something else was missing, is now OK again.