Cutting the subplots does help tremendously (Plankton goes easily), but you run into two problems with this format. One, this essentially reduces the story to an external-only conflict: stop the volcano and save Bikini Bottom. None of the characters experience any internal conflict (granted it's a theme park show, but, that's what Broadway presentation does well). Hero is my Middle Name doesn't work without the anti-science/mammal material to drive a wedge between Sandy and helping. The Boogie subplot doesn't go anywhere without Squidward's self-doubt and his triumphant (and delightful) I'm Not a Loser number. And really, the benefit concert doesn't hang together without the broader story...
It's all moot anyway - as someone up there pointed out, the show's going on tour. There's definitely a version of it that could work, but I'm not sure this is it.