deploy: Change large parts to be fd-relative, drop fsync

deploy: Change large parts to be fd-relative, drop fsync

This is a continuation of earlier work to drop the individual fsync on
files/directories in favor of relying on `syncfs()` for speed.

As part of that cleanup, I'm porting it to be fd-relative.

I feel relatively confident about this change given that this area of
the code has notable test suite coverage, although that code runs as
non-root.