Git: How can I find a commit that most closely matches a directory?

you could write a script, which diffs the given tree against a revision range in your repository.

assume we first fetch the changed tree (without history) into our own repository:

git remote add foreign git://…
git fetch foreign

we then output the diffstat (in short form) for each revision we want to match against:

for REV in $(git rev-list 1.8^..1.9); do
   git diff --shortstat foreign/master $REV;
done

look for the commit with the smallest amount of changes (or use some sorting mechanism)

This was my solution:

#!/bin/sh

start_date="2012-03-01"
end_date="2012-06-01"
needle_ref="aaa"

echo "" > /tmp/script.out;
shas=$(git log --oneline --all --after="$start_date" --until="$end_date" | cut -d' ' -f 1)
for sha in $shas
do
    wc=$(git diff --name-only "$needle_ref" "$sha" | wc -l)
    wc=$(printf %04d $wc);
    echo "$wc $sha" >> /tmp/script.out
done
cat /tmp/script.out | grep -v ^$ | sort | head -5