We cut the mortises in our chair seats with a plunge router. We use a guide bushing fastened to the router and a fixture clamped to each seat in turn. The splats have no shoulder; we have to precisely fit each one to its mortise by hand or a gap will show. The first fixtures I built to guide the router were made of plywood. As careful as I was to make each opening (and therefore each corresponding mortise) exactly the same, imperfection in my making (and wear over time) yielded slightly different mortises. Therefore, we had to be sure all splats were cut large enough to fit the largest mortise, making extra work to fit the smaller ones. We have spent a great deal of time over the years fitting splats and figuring out how to spend less time fitting splats. To get mortises of consistent size, we hired a machine shop to build aluminum plates for the dining chair and rocking chair fixtures . . . a great success. The mortises are within a few thousands of each other.
