@jaffathecake I wonder if there's a path to something like shadow DOM slots? In that context you can "project" an element from one location to another. What if the browser did a similar trick but which duplicated the element visually, while still only having one element in the DOM? Similar to how projected light DOM is not *in* the shadow DOM, it has a slot linked to the light DOM.
That feels similar to your last option but maybe would be more feasible to browser maintainers? It might require it's own spec independent of styled `<select>` though.
I wonder if that would help with something like `<canvas>`, since you could keep the same visual content in both copies, as there is only one source of truth. Doing this with an iframe sounds weird and scary though, so maybe it's a bad idea.