This might work. Follow these some or all of these instructions. The instructions are how to run multiple Debian services as separate LS instances from one installation. You will not need to do the last bit i.e. from plus SERVICE_NAME and SERVICE_DESCRIPTION onward.
Remember to use local disk for the LS data and log folders. Config can be on the shared mount but keep separate.
Also, check that bin/logstash.lib.sh is detecting the shared mount paths in the local context correctly.
Good luck - to my knowledge this has never been tried.
OTOH - why not use Ansible, Chef or Puppet to install a preloaded copy of LS?