Thanks to the link in Xavier's answer I learned that I can override the gpg program with the gpg.program configuration:
git config --global gpg.program /path/to/something
So I can use this to write a wrapper around keybase.
But git is, as it turns out, pretty finicky about what that something is. Git expects to partially parse the output that results from the --fd-status flag, which causes gpg to output special status codes at an alternate filehandle.
Fortunately, at least for my first pass, git doesn't parse everything that gpg produces, so I was able to emulate it. Here's a gist with a functional wrapper, and here's the meat of it:
# Copy the commit message from stdin to a file. 
d=$(mktmp -d "${TMPDIR:-/tmp}/gitsig.XXXXXXXXX")
cat > "$d/commit.msg"
# Have Keybase write the signature to another file.
keybase pgp sign --detached \
                 --key "$1" \
                 --infile "$d/commit.msg" \
                 --outfile "$d/commit.sig"
# Have gpg verify the signature right away.
# Capture its status in a file.
gpg --verify --status-fd=2 \
    "$d/commit.sig" "$d/commit.msg" \
    > /dev/null 2> "$d/gpgstatus.txt"
# Copy the KEY_CONSIDERED lines to stderr. Git wants that.
grep '^\[GNUPG:\] KEY_CONSIDERED' "$d/gpgstatus.txt" >&2
# Produce a minimal SIG_CREATED line to stderr. Git also wants that.
printf '[GNUPG:] SIG_CREATED ' >&2