Whelp, I figured it out. I set up a multicore environment following this article (definitely don't use spaces in the core name), and using the sunspot_rails configuration found here. For clarification, the path:
reference in sunspot.yml is essentially what gets tacked on to the URL when referencing a 'core': i.e., http://mydomain.com:8080/solr/production (emphasis to indicate my point).
So now I don't have to care about running the rake task to start Solr because it's always running all 3 cores on boot through a single instance of Solr via Tomcat.