Now was the time to delve really deep. Now that I had the layout figured out, I needed to make the mechanism actually function. If you’re interested, the theory is in the photos down below!
In case you can’t read my horrendous handwriting:

1. The hot air moves to the center of the Stirling engine.
2. Because the hot air moves to the colder area, it becomes colder and compresses. The compression moves the power piston.
3. The cold air is then shuttled by the displacer to the hot end. The cold air becomes hotter and expands, moving the pistons and flywheel. The flywheel’s angular momentum continues to move the pistons, returning the cycle to its first stage.

Throughout steps 2-3, the flywheel keeps the momentum and continues to move the pistons. Unfortunately, I haven’t pictured the flywheel in relation to the engine, but you can imagine that the flywheel is at the axle of the crankshaft.

So, from what I knew, the cranks of the pistons needed to be, optimally, 90 degrees offset, with the displacer piston 90 degrees ahead so that it could shuttle the air first.
Then, using the diagrams I drew below, I configured one of the phases into Onshape to hopefully create a working mechanism.
The design is still in the works, but I think I at least have a nice working structure! :)