I don't think so since the top are required to help grow the potato's. they don't kill of the tops in commercial fields ever they just wait till they naturally die back then harvest. I would suggest covering the plants with straw so that just the top leaves show and you should get more potato's of all sizes.
I would never stomp any plant that will shock the plant stop root growth and release a hormone that will trigger the plant to flower and seed to preserve its existence. I would try using a more airy soil medium. Your problem could be there is too little oxygen in the soil or too many obstructions such as rocks and large pieces of mulch. Shredded pine bark, happy frogs soil conditioner and perlite are all good amendments to provide more air in the soil. Also foliage growth is due to nitrogen mainly so try lowering you nitrogen feedings and increase phosphorous because this is the main nute for root growth also microbial life such as mycorrhizae is always a great addition to develop healthy roots. If you have any additional questions I love helping let me know!