Unfortunately, topping and cutting back to bare wood is the least desirable way to keep  small or short a mature plant that naturally grows to as much as 15-30 feet (depending on which cultivar of Prunus laurocerasus you have). Your photos show tall , bare stems on most of the bushes. The type of cutting you describe works fine on the tips or outer edges of the plants, but it is not viable for shortening the hedge. Under no circumstances would you want to even attempt to cut back this shrub in the heat of summer. Our best solution to your problem offers you two options: (1) remove the English laurel and start over with something else or a shorter cultivar of English laurel , or (2) plant  shorter, bushier plants in front of the laurels on your side of the hedge. Keep them maintained at the height you wish. Some suggested plants would be Texas privet( Ligustrum japonicum 'Texanum') which grows to 8 feet, Hybrid Yew (Taxus x media 'Brownil') also 6 to 8 feet, but a slow grower; or one of the Evergreen viburnums, such as V awabuki; V. x pragense,or V.tinus.(all small-leafed, prunable plants that have the bonus of flowers.) Once these shorter bushes are established and growing well, you can begin to remove the laurels. We know you need to keep in the good graces of your neighbor, but it isn't their problem nor their right to dictate how high they want the hedge on their side , unless they shared the initial expense of planting the hedge and/or have a mutual understanding to maintain it. A tip for planting any new hedges between neighbors: always keep the plant far enough on your side of the border line so that you can maintain it from both sides while remaining on your own property. Good luck  with your new plant adventures!