Hi,
no worries, I got too many things on my plate as well. I haven’t used 2 Docker containers for running GitLab and the runner yet, so I am guessing a bit.
During my search for docker-compose gitlab runner register I’ve found this issue with a suggestion to move the register portions into a script.
Also, it seems that your docker-compose configuration does not define a shared network between the two containers - which might be the overall culprit here.
You probably have found this gist which seems old and dated. Maybe start from scratch with the above linked example? 
Cheers,
Michael