I am responding to myself here.... I have managed to solve my problem (detailed above) so I thought I should write explain in case others have the same problem.
libc6 and base-files are very imporant packages so even if I could have removed either of them it would totally screw up my box and make it unworkable. The problem in my case is a bug where both of these packages are trying to update lib64. I found some information plus a solution at this link, along with the responses:
Since I have a pure64 system it is safe to do a force-overwrite like this:
dpkg --force-overwrite -i /var/cache/apt/archives/libc6_2.3.2.ds1-126.96.36.199.pure64_amd64.deb
(Actually the first time I typed this it didn't work - clumsy fingers perhaps. But the second time with tab-completion on the file name it worked.)
Hope this is clear enough.