Well, I got it imported, but not using BigDump.
(That's the first time that it's failed me.)
Actually it failed three times without proper error identification.

So I tried mysqldumper which gave me the sort of alert I am used to receiving from BigDump. (I wonder if something has changed in BD?)

Anyhow the problem was that when trying to save ubbt_SAVED_QUERIES I was getting a 'Field can not be NULL' alert.

Well, that's easily rectified by deleting all my queries (the dbase is way too big to search through all the text, just to remove the one). They can be restored manually easily enough.

Anyway I know this is verbose, but in the interests of anyone else experiencing difficulties, it's always good to make records of what happened.

By the way Giz, I know that you don't like or approve of this method, but I really think that you should consider people who don't have shell access when writing your transfer/ upgrade tuts. Not everyone is in your position of having shell access. Not everyone wants to change hosts for this reason.

Alternatively, if you aren't interested - I will do it and make reference to my experiences.