I can't figure out how to allow visitors to continue to view our current (wordpress.com) site while I edit our new (wordpress.org) site.
You need to keep the nameservers set to WordPress.COM and use a different domain name on the new site until you are ready to switch over. You can't use a domain name in two places, no.
GD might be able to give you a temporary domain to use - so ask them about that.