I hardly know anything about MFX, so hopefully Diki or someone else will chime in. However... if the MFX settings are stored with a "performance" (User Program), then there are ways to set up a foot pedal or push button that will call up a specific performance when pressed. You'll have to use performance holds to prevent other things (like the style) from changing, but it will achieve your intended effect.
Of course with all of those performance holds enabled, it will prevent you from using performances to change other while playing a song. So you will have to rely on one-touch settings or favorite tones for that purpose. My $.02.