As alggag & jasonvr have noted (and others no-doubt will), there really is no workable/practical solution to your particular situation. In addition to not having lots of air service, Boise is geographically disadvantaged from the Caribbean/Mexico.

At a quick glance, Southwest serves Spokane, Oakland, Sacramento, Denver, Chicago, Las Vegas, San Diego and Phoenix non-stop from Boise. That's it.

Significant international service (by Southwest's standards) is mostly via Houston, Fort Lauderdale & Baltimore.

A crude work-around would be to fly from Boise to one of those stations (which will currently require at least one stop), spend the night, and then fly to your desired international destination. Some semblance of the reverse-process will likely be necessary to get you home. Whether or not this sort of round-robin config is worth your while or not (financially and time-wise) is an individual decision.

It seems unlikely that the pending computer "upgrade" planned for May 9th will do anything helpful for you as the actual flight schedules out into the future are already published.

Although they'll be happy to talk to you, "calling" will accomplish nothing you can't do yourself as there are no secret work-around routes available to the Agents that you cannot access yourself.

Sorry for the lack of a silver bullet.