Wow. After 20 minutes I had to cancel the browser tab.
However, along the way, watching with my FTP client, I was able to see files in WP-admin, WP-includes and in my root are updated to today's date. Once I saw all files with today's date, I assumed that all new files are uploaded. So I went to a new window and started another WP Admin session, and on the Dashboard it says I am on 2.8.5, with no more message to upgrade. The site seems to be working normally (knock on wood).
Does anyone know if the last thing the upgrade process does is to set the new release number? If so, I'll know it's done.
wp-content/upgrade still has the new release files in it, don't know if it's supposed to delete it or not.