In this article I'm going to refer to the web client, but the process is identical for SBA.
To recap:
Internal web site for the web client. Public domain name. Public cert. Just to be clear, the web client will only be visible inside the firewall, the fact that the domain name is public will not matter. Trust me.
The steps outlined below are before the web client install. If you've already installed, you'll need to uninstall and reinstall.
So, go out and buy a domain name. Personally, I use Network Solutions, I have for years. In our example we're going to use MyGP.com. Then, go and purchase an SSL certificate for MyGp.com. We'll cover that process in another article, we're only covering the networking in this one. Be sure that you understand that www.MyGp.com is different than MyGp.com. I recommend the simpler one, less typing.
Log onto the box that hosts your DNS.
Open the DNS applet. On my Test Domain Controller, the box name is job.devshed.local. That's Job with a long O, because he's long suffering. You might have to Google that. <smiles>
Right click on Forward Lookup Zones as shown, add a New Zone

Work through the wizard, take all the defaults.

Defaults

Defaults

Add the name of your URL, as shown.

Defaults

Done.

You'll get the screen below. Add a new A record.

Here's the thing. Carefully leave the name blank, and add the IP address for the server hosting the web client, as appropriate.

When it's done, you'll have the result below; you should be able to ping the URL as shown.

Now that you have the domain name and the cert, proceed with the web client install. Be sure to use the newly installed SSL cert.
This is all new and largely undocumented. I'd really value any feedback.