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I threw this animation together rather quickly, so the conrod doesn't connect properly, but it shows the concept. The idea is to have the displacer bottom out about 15 degrees before BDC. The cold side of the displacer will have a diaphragm the con rod attaches to. As the displacer bottoms out, the air inside gets heated and compressed, once motion passes BDC, the diaphragm would give a bit of kick before the displacer leaves the bottom of the chamber. Sort of a hot air engine within the stirling.
This seems to approximate a "perfect stirling cycle" a bit better, though the power piston's movement is not affected. Could give an extra 5-10% efficiency, in my dreams. Could be the forces working against each other cancel out. Only way to know if it helps is to build one, but I would appreciate any comments.