I have seemingly solved this issue. I failed to copy /lib/libnsl.so.1 into my chroot /lib folder but have added it and I can start nginx using the start-stop-daemon command with the --chroot flag; strace is a life-saver.

In case anyone else goes down this road in the future, you can strace your start-stop-daemon call to a chrooted nginx as follows:

# start-stop-daemon --start --pidfile $PIDFILE --exec $DAEMON --chroot $CHRDIR --startas /usr/bin/strace -- -f -o /tmp/$NAME.strace $DAEMON $ARGS

where...
$PIDFILE = path/to/nginx/pid
$DAEMON = /usr/sbin/nginx
$CHRDIR = /chroot/nginx (or your chroot dir)
$NAME = nginx

make sure you copy /usr/bin/strace into $CHRDIR/usr/bin/ else the above command will fail (don't forget to remove it after you've debugged everything).
strace will be output to $CHRDIR/tmp/$NAME.strace.

This is how I was able to determine what libraries I needed.