I see lots of posts about opkg failing due to DNS ... but I'm pretty sure that's not the case here. DNS is working fine ... but I think the issue is trying to get opkg to pull from,
https://www.mydomain.com:4443/
I have to use the custom port number as 443 is not available - and thinking that's what is causing the grief here? Has anyone seen this, and/or been able to get it to work?
You said that the server is behind your OpenWrt router, right? If that's the case, you can run the server with port 443. Then, if it is necessary to access externally, you can port forward 4443 > 443, thereby avoiding the issue with the port that's in use by AT&T's gateway.
Once that's set, you can simply use the lan IP address of your server and/or you can create a local DNS entry for your domain so that it connects to the local IP (rather than the public IP) and therefore doesn't need to deal with the unusual port number.
If these are not options, have you tried specifying the port in the feeds URL?
When I specified port 443, it worked without issue (the server does use port 443). Specifying port 444 (as shown here) causes it to fail (expected here because the server isn't using port 444).
That suggests that the port numbers are respected, provided that you included them in your url structure.