Remember “Blow” by Kesha? (Yeah, me neither till yesterday—thanks @Angela—but now that I mention it yes.) Anyway, her song also tackles a similar problem of monotony—that synth bass is there doing more or less the same up-and-down slide for the whole track, with the exception of the bridge. Her solution is twofold: at the start of the second verse (“now what? we’re taking control”) she runs the bass synth through a stereoizer and then processes each half slightly differently, and then at the end of the bridge she has it “stutter”, so the sound is recognizably doing the same sorts of things, but with variation—I think probably this was accomplished during recording, but a delay or granulizer plugin could do something similar. In this vein, it might be fun to split your drone into a couple channels and throw slightly different effects on them, and then add some gentle automation motion.
(I’m aware that Kesha probably does not work directly on the sound design of her songs, but it’s both convenient and kind of fun if you’re in on the joke to refer to the massive corporate conglomeration behind her music as being literally her)