My gut says that either Zapier or Integromat could be used to pull in this data. Both have free accounts, and both have means to let you call external APIs and process the returned data. Integromat also has some built-in Facebook integration (including an action called “Get Post Reactions” that may be useful). Zapier has some Facebook-related actions, though by their names they don’t look relevant to what you want. You may be better off just calling Facebook’s own API and processing the return.

I’m also interested to know if this is possible with scripts. If one of the experts could pitch in on the feasibility, I’d be more than glad to be involved in creating one

I haven’t tested it, but my gut says that a script should work, either in the Scripting app or via a script action in an automation. It’s like any other API call. Pass the proper request and it should return the desired result.