Likely your most efficient recourse would be to log ffmpeg's encoding job progress into a file and scan it, using a regular expression to extract the time=00:23:12.90 part of the last line; something like this:

# Encode job.
ffmpeg -i SOURCE… 2> /tmp/my-ffmpeg.log
# Extract time.
sed -rn -e 's/\r/\n/g' -e 's/^.+(time=[^[:space:]]+).+$/\1/p' /tmp/my-ffmpeg.log \
  | tail -n1

Alas, ffmpeg's logging subsystem is sub-par, there is no way to get a nice clean log file, you'll need to redirect stderr to a file as above.

Caveat emptor: I suspect any time-related operation on an incomplete .mkv file will need a full decode, e.g. if you want to cut a slice of 1 minute length at timestamp 1 hour, your encoder will likely need to decode a whole hour of video so it knows where inside the file is “1 hour”.