Not quite what you're asking, but if it's important for the ffmpeg job to finish, it might be enough to renice it to give it a lower priority than the web server processes.
Run something like
ps auxw |grep ffmpeg to get the PID of the ffmpeg process, then issue
sudo renice -n 19 PID to change the process priority, for process PID from the first command.
This strategy might work a little better than outright killing ffmpeg. It'll give you breathing room for the web processes, but will allow the original job to finish. Also, if there's some sort of job queuer running, it may just start up ffmpeg again after it sees that the original job did not complete successfully.