Yep, it looks like you have it OK now.
Most of the transponders are listed on Lyngsat, so if I were you, I'd check out all the channels you want on the NON-sky box before proceeding.
The only only extras you will get on the Skybox are Sky 3 and the FIVE channels.
You already have ch4, (8350 I think). You don't need a Sky box for the ITV or BBC channels.
Since you appear to be getting Astra 2D OK, you should be good for everything else.