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I don't even know if such an animal could be built. So this is just a hypothetical question like the carnot cycle. What if the displacer could turn on and off. Exposing heat at the right time then concealing it at the cold end. What Iam thinking about is a displacer regenerator which is an insulted hollow cylinder, open at the bottom. Then filled with steel wool. Some sort of mechanical switch opens then another switch closes an insulated door at the bottom opening. Perhaps a half circle, witch swirls closed to seal in the heat. Then swirls open to expose half the bottom. The switches could be knobs sticking out on the inside of the cylinder .The mechanics arent important at this point, just the concept. As the displacer moves up towards the cold end ,when the bottom of the displacer reaches dead center, the door closes concealing the heat. As the displacer moves down, when it reaches dead center it opens .It releases its heat till it reaches the point when the hot end is hotter, then it begins to absorb more heat. The displacer would reject little heat at the cold end but retain it for the hot end.

I wonder if this proposed design reduces the regenerator's dead space or simply shifts the dead space to inside the displacer.

In the displacer cylinder, at the hot end, fins have been used to increase the surface area. The hot to cold passage of air should, for efficiency be diverted through a regenerator. In a simple engine the regeneration takes place along the length of the displacer. Ian S C