With baited breath, I waited for the DNS to update for the Bourke Aboriginal Health Service, and am extremely happy to report that the site has now gone live successfully, and their email still works.
No reason it shouldn't have, but after a major email outage after their last DNS update a few years ago, I'd been warned that they'd had little success and that I should proceed with extreme caution.
I received an email this morning from Judy Johnson thanking us both for our generosity to their organisation: "we all appreciated the hard work done by you both".