How to clean git log when removing unwanted files with BFG Repo-Cleaner

Question

I am trying to clean up a git repository by removing a number of files and folders with the easy to use BFG Repo-Cleaner. It removes the files and folders well (Thanks!) But the git log now has a number of commits with no file changes.

How can I also update the history so that commits made empty by file removal are removed?

Additional notes:

• This is possible with the more awkward filter-branch approaches (e.g. this answer) with the --prune-empty option as described in github's how-to.
• The approach of cleaning all empty commits (e.g. this answer) after the fact did't work well because: (a) there are some legitimate no-file commits in the repo left from old SVN tags, and (b) doing so also seems to strand some branches.