On IIS 7.5 I am trying to achieve this with two websites:

Default Web Site is bound to:

(blank host header port 80 - http)
(blank host header port 443 - https)
go.example.com
www71.example.com
the IP address of go.example.com

2nd web site "Beta" is bound to:

beta.example.com
(blank host header port 443 - https)
* using blank only because it doesn't seem to be possible to 
  bind https to a named host header

And both need to work with SSL. But I have these problems:

1. When I type in beta.example.com, I see the go.example.com site instead
2. I can not seem to add the SSL binding to both websites at once (I have a single *.example.com wildcard certificate). The beta site will not even start if I add the https binding to it.

This is how I have set it up:

What is the correct way to set it up?