Minimal Cushion Shoes
Minimally cushioned running shoes are designed for those looking to build and maintain any level of mileage through consistent, long-term effort, for walkers looking to strengthen their whole-body health, and for folks looking to improve their muscular base. Minimally cushioned shoes feature a low level of cushion that transmits feedback from the ground directly to the foot itself. Minimally cushioned shoes have traditionally been associated with racing, faster training and functional fitness workoutss, but can be used for a wide variety of activities with proper preparation.
Minimally cushioned shoes provide the least amount of cushion between the foot and the running /walking/standing surface, maximizing the amount of feedback received by the foot and - as a result - increasing the foot's ability to strengthen over time. Minimally cushioned shoes promote proprioception (the foot's feel for the ground) and provide a level of protection from elements while more closely replicating the shoeless experience of the past. Minimally cushioned shoes at the Ultra Running Company have 22mm of cushion or less.
BUT Here's A Huge Problem:
You've found the one path that breaks the system. The enhanced ground feel provided by little to no cushioning would be completely ruined by adding such a high level of extra cushion under the heel, so no one makes a Road shoe with High Drop and Minimal Cushion. Perhaps you could check out the other options available?