> IIUC, your solution should work but it's necessarily tied to specific
> export backends, right?

It is partly but the general concept of using special blocks works for
HTML also.  You end up with code that looks like this:

,----
| <div class="myquote">
| <p>
| and this is the inner block
| </p>
|
| </div>
`----

which means you can customize its appearance using appropriate CSS code.