I also have a TiGoat bivy with full net hood courtesy of a BPL member. Mine also has a 24" side zip. The side zip doesn't add a zipper. The zipper just continues down the side. It is a two way zipper. The net hood zipper is one way and just goes across the chest. Both the net hood and the outer hood have pulls attached for tying the hoods up and away from your face. I have about 18" between my face and the hood in that case, or enough room to hold about a map. The hoods should be used individually. Either rolls or tucks back when using the other. You could have the net hood extended inside the outer hood, but it would block access to the zipper pull for the outer hood. You'd have to unzip the net hood before you could unzip the outer hood, and the net hood serves no purpose when the outer hood is in use. The zippers are not of the waterproof variety used on rainwear. There is a storm flap on the outside of the outer zipper for water resistance, but the fabric is not waterproof, only water resistant, so I don't think you'd want to have the bivy as your only weather protection if rain was a possibility. The bivy is roomy, enough space for my long Marmot Sawtooth 15 degree winter bag.
Below are some pictures illustrating the various ways the hoods can be pitched. That's my sleeping bag inside for contrast.
Here is the net hood only. The shiny black material at the bottom is the inside of the outer hood folded back.

Here is the outer hood picthed.You can see the storm flap and two zipper pulls. 
Here is one of the options you asked about. The outer hood mostly pitched for splash protection but space left for breathability and still using the net hood.