A button doesn't have to be inside a form, though. You could have an empty form as a neighbour to the button (or anywhere else inside the page body), and associate the button with it.

  <button form="logout-form" ...>logout</button>
  <form name="logout-form"></form>

No layout implications that way, barring any nth-child css (solvable by putting the form somewhere else). Doesn't solve the form being limited to GET/POST, but styling concerns are atleast handled.