How can you completely eliminate the vertical component if the cart has vertical compliance? Tell the coils not to respond to those movements?
Seems like that's exactly what's attempted, either by connecting stereo MM coils in series, or orienting a coil for lateral movement. Vertical rejection might vary depending on design, but I certainly wouldn't play even a pre microgroove record with a stylus with no vertical compliance.
I believe a "properly" designed mono cart will eliminate objectionable stereo differences between channels and vertical noise will be down at least 30dB. A mono switch might also give 30dB rejection, but stereo differences will be blended, not eliminated.