It's really odd that the cleats are wearing out this fast. But your idea is good of switching to "two hole" cleats (Shimano SPD, Crank Brothers, Time ATAC, etc. etc) which can be used with shoes with bottom tread (usually called mountain bike shoes, but also touring shoes, gravel shoes, etc). A lot of these type of shoes are as good for sole stiffness and as the best road shoes, and are still highly walkable. I have Sidi Road shoes and MTB shoes and they are virtually identical except for the tread on the MTB shoes.
.