First the
"country"
and
"State"
combo box willl not change.
If you use alt down arrow to open them, you just hear
"Edit."
And if you toggle browse mode back on, you're yanked back up to the top of the ckecout page.
This is with NVDA 2017.1 and Firefox 54. I've not tried edge, as accessibility there isn't great from what I hear.