That would necessitate a redesign/ strengthening of the structure to handle the increased weight. The center of gravity would be father forward with the heavier engine, and moving the engine rearward wouldn't be terribly simple because there is little clearance after the pilot's feet to take away length to bring the engine closer. The fuel burn would increase, meaning you would want more fuel, which adds more weight. The wings would have to be redesigned for the new gross weight of the airplane, and the landing gear would DEFINITELY need to be made stronger the handle all of this. The tail structure would have to be beefed up to handle the larger aerodynamic loads from a faster speed, etc... At some point, it's better to find a design closer to what you want than it is to so completely change an existing one, unless you're an engineer with the right knowledge and resources.
The aircraft's Never-exceed speed (Vne) is 85 MPH. A 4-cylinder would almost certainly place Vcruise above Vne. If you're looking to make an Legal Eagle a fast single-seat LSA, it might be better to talk to your local Designated Airworthiness Representative and ask what they would want to see on a Legal Eagle to get it an LSA airworthiness certificate, then build a legal eagle with a 37 or 45 hp cut case conversion and a covered fuselage. Even then, I would caution you to seek the right advice on the engine mount and structural considerations because you could end up bumping up the Vne past the 85 Mph of the original design.
