I can indeed (for now) locate the issue to the following command:
git ls-files -z | xargs -0 tar -c | tar -t -C ~/tmp-circleci
Signal 13 means the second tar is still reading and the first would be finished writing. (cf https://stackoverflow.com/a/27903078/2367848, which I guess you read as well)
Edit: this seems to work with a test repository with only 1 file (committed). The copy happens w/o error. Maybe a problematic file?