Thanks for the confirmation, this matches my expectations. Sadly this is not great for those running these old versions.
So my initial statement still holds, right now there is not much that can be done for CentOS/RHEL 6. I strongly recommend upgrading, if that's possible in any way shape or form.
Otherwise, I don't know if there's still someone willing to support this OS, but if there is: It may be possible to backport the partial/alternate chain behaviour of 1.0.2 to 1.0.1*, which could enable "remove-the-old-root" workarounds. This requires patching OpenSSL though.
Using LE's short alternate chain is definetly a fix, if all servers are under your control and old Android compatibility is not required.
*I just made a trip to the source code. The basic commit that enables the 1.0.2 workaround was this one, but you can't backport that directly, because a) the code on 1.0.1 is slightly different and b) there were issues with that code, later fixed in followup commits (one, two, three + at least three more). May be easier to just update everything to 1.0.2...