Remove stat dependency

This is, strictly speaking, a downgrade in functionality, with the
upside of reducing reliance on non·Posix programs (namely `stat`). A
better, Posix‐compliant solution is to archive an empty file with the
correct modification time and then list out the time from that archive;
however, as far as I’m aware, it’s not possible to obtain an
implementation of the `pax` utility which actually supports this. macOS
only supports a very limited subset of the `listopt` option, and only
for pax archives (not tarballs); other implementations don’t seem to
support it at all.