I think I've identified what's causing the error on my end. If I click the 'continue' text link all the way through the checkout process it continually loops on the confirm address page. However, if I instead use the -> arrow (beside the text 'continue' link) the checkout process proceeds to completion.
My issue was not that I could not figure out how to download (once the ordering cart process advanced it was fairly obvious), but rather an issue where the cart would never advance to the My Downloads order details page.
Thanks for the response.