In an effort to avoid filling $TMPDIR with stray files, let's close all
Tempfiles after we are done with them. Additionally, add an around-filter to
each test in the integration suite to catch cases where we don't do this.

This exposes issues around re-processing a subset of our attached files: it
leaves Tempfiles around. Mark that test as skipped (with a detailed
explanation) because we cannot figure out how to make it work.

Related to #1326.