Incremental import of git-fast-import stream to Mercurial?

Question

I am in the process of converting a few older repositories and splicing and dicing them as needed to get one future repository. A bit of scar tissue in the history (most of them due to semantics in the previous VCS) had to be removed as well, but all in all the conversion seems to be smooth.

It just takes very long.

Background: I am using reposurgeon, which works based on git-fast-import streams. Target format is Mercurial.

How can I import new increments of code introduced into the old VCSs while they are still live, such that I don't have to run through the full conversion routine every time?