create structured clone of Proxy

I have a class that returns a Proxy from the constructor. When I try to store instances of this class in IndexedDB, or send the object using window.postMessage(), I receive an error stating that the object could not be cloned. It appears that the structured clone algorithm cannot handle Proxy objects.

The following code demonstrates the error:

class MyClass {
  constructor() {
    return new Proxy(this, {
      set(target, prop, val, receiver) {
        console.log(`"${prop}" was set to "${val}"`);
        return Reflect.set(target, prop, val, receiver);
      }
    });
  }
}

const obj = new MyClass;

try {
  window.postMessage(obj,'*');
} catch(err) {
  console.error(err);

}

Can anyone suggest a workaround for this problem? I see two potential solutions, but I don't know how I might implement them:

1. Do not return a Proxy from the constructor, but maintain the Proxy functionality within the class declaration somehow.

2. Alter the Proxy instance so that it works with the structured clone algorithm.

EDIT: The following, simpler code also demonstrates the structured clone error:

const p = new Proxy({}, {});
window.postMessage(p, '*');