While Writing this question I fiddled around some more and found a solution, but since I haven't found a similar question with a working answer so far, I decided to post this question anyway, including the answer - I hope that's ok.

For some reason, setting the environment variables using solr.in.sh doesn't work. However, setting them via compose's environment:, works just fine, so just adjusting this block to

environment:
      ZK_HOST: [SELF-IP]:2181
      SOLR_OPTS: -agentlib:jdwp=transport=dt_socket,server=y,suspend=n,address=*:5005 -Djetty.host=[SELF-IP]
      SOLR_TIMEZONE: Europe/Berlin
      SOLR_HOST: [SELF-IP]

worked out sufficiently, no host-mode required.