I have been able to play with stirling engines quite a bit and have looked into using big stirling engines for many projects that I have dreampt up.
In theory it would be amazing to do what you are proposing, but the reality is that it wouldn’t work well. The biggest problems that plague stirling engines today is that they they weigh a lot and need a VERY big displacement for their power output. So a 10 hp stirling engine would likely weigh well over 30 pounds not to mention the crazy big radiatior that you would need to keep the cold side cool enough to have any decent efficiency. Other problems with the stirling engine include bad throttle response, they need to use helium or hydrogen as the working fluid to be efficient which comes with many additional challenges, and very little development has been made with the stirling engine.
Efficiency wise, gasoline spark ignition engines have a theoretical energy efficiency of between 56 and 61%, a paramotor engine at a cruise is somewhere in the range of 15% efficient and the world’s most efficient spark plug gasoline engines are about 35% efficient (not counting any engine with a pre-chamber or compression ignition). So just because a stirling engine may have a 67% theoretical efficient doesn’t mean we are anywhere close to it. As far as I know the most efficient stirling engine was made by nasa and it was “only” about 40% efficient.
So by the time you have a 10hp engine with a massive radiator, you will be over 60 pound if you are really luck and you would still need about an extra 40 pounds for the frame and electric system plus 15 pounds of fuel. All for a paramotor that would be more maintenance intensive, less reliable, and less powerful than a 35 pound vittorazi moster engine.
Here are a few stirling engines you can look into to understand what sort of power a stirling engine in the weight and displacement range of a 25hp vittorazi moster is producing:
This philips stirling engine only produces 300 watts of power (not even 1/2 horsepower) and I know it weighs well over 40 pounds.
This one was custom built. It is 127cc and produces 700 watts of power (almost one horsepower) and it weighs about 40 pounds