This is a great thread! Gave me the starting point to fix my issue, hopefully it helps someone else.
I have had Subsonic since 4.6 and it used to have a field for a custom domain. I was a bit ticked that its been removed now that I updated. I have a real SSL installed and configured and want to leave it all SSL without any 4040 http nonsense, but I still want to use the sharing feature. I am on Ubuntu so I just installed apache and made sure 4040 wasn't in use on Subsonic. I enabled the something.subsonic.org setting in subsonic and forwarded port 4040 to apache in the firewall. In a shell I enabled mod_rewrite:
sudo a2enmod rewrite
(restart apache)
Made a new Virtual apache host file, put in /etc/apache2/sites-available with this:
Listen 4040
<VirtualHost *:4040>
DocumentRoot "/var/www/html"
<Directory "/var/www/html">
AllowOverride All
</Directory>
RewriteEngine on
RedirectMatch ^/share/(.*)
https://subsonic.mydomain.com:4443/share/$1</VirtualHost>
(save, restart apache)
Now shares are correctly redirected to my domain with SSL, no SSL mismatch errors, and no changes needed to Subsonic, life is good.