... But the whole point of playing a style is switching chords while you're playing... So what's the point of playing the Song with a predefined chord progression along the style?
I might be missing something, but let me suggest the following approach: How about making a style out of your song and playing along? You can create a Style with one variation, use the CASM section, and define an NTT/NTR as "Root Fixed/Bypass" for all the melodic parts (everything but the drums/percussions). In this case, the same chord progression will play over and over again. This resembles DJ styles found in modern Yamaha Keyboards in the sense that they also define a chord progression rather than a single chord that can be triggered by a left hand