You can either Proxify a class or an instance of a Custom Element.
Given the following Custom Element definition:
class A extends HTMLElement {
  constructor() {
    super()
  }
  connectedCallback() {
    this.innerHTML = 'Hello'    
  }
}
customElements.define( 'a-element', A )
Proxy for a Custom Element instance
Create a Proxy from an instance reference (here: ae): 
<a-element id="ae"></a-element>
<script>
  var b1 = new Proxy( ae, {
    get ( target, value ) { return target[value] }       
  } )
  console.log( b1.innerHTML ) // => "Hello"
</script>
Proxy for a Custom Element class
Define the construct trap to catch the new operator:
<script>
  var B = new Proxy( A, {
    construct() { return new A }
  } )
  var b2 = new B
  document.body.appendChild( b2 )
  console.log( b2.innerHTML ) // => "Hello"
</script>
Get a Custom Element instance Proxy from a class Proxy
If you want to instanciate a Custom Element and get one Proxy object directly, you can combine both solutions above.
The following example shows how to get a Proxy for element <a-element> that will log in the console each property access. The construct() trap defined in the class Proxy returns itself a Proxy for the instanciated Custom Element.
class A extends HTMLElement {
  constructor() {
    super()
  }
  connectedCallback() {
    this.innerHTML = 'Hello'    
  }
}
customElements.define( 'a-element', A )  
var P = new Proxy( A, {
  construct () { 
    return new Proxy ( new A, {
      get ( target, value ) { 
        if ( value == 'element' ) 
          return target
        console.info( `proxy: property ${value} for <${target.localName}> is "${target[value]}"` )
        return target[value]
      }       
    } )
  }
} )
var p = new P
document.body.appendChild( p.element )
console.log( p.innerHTML )