If you are planning on using the ms60b for this specific purpose, then i'd recommend downloading the zoom effects manager. It basically allows you to upload any of the zoom effects to the unit, not just the bass effects. you can load it up with all the EQs and pre's that zoom offer and see what ones work best. Just remove the flanges and delays etc that you wont use. Some of the non-bass EQ's might work better for you.
Although could an 8th turn of the tone knob on the bass tame the harsh end? I'm guilty of thinking a pedal is needed when actually a tweak on the bass can make a change!