There is a button at the top of the new homepage, visible to screen readers, that will let you opt out of the new design. See
$1 between myself and Reddit admin /u/ggAlex. We've been promised shortcut keys and correctly labeled buttons. While I can't speak to if these promises will be kept or not, I can say that several minor issues were fixed in the alpha, before the beta launch. I have also delivered more detailed feedback in private messages to the Reddit admins. If you wanted me to guess, based on the current pace of progress, and the previous behavior of Reddit, I'd say we've got about a 75 percent chance that the new design will be fully accessible by the time old reddit is disabled, whenever that happens.