We have a screened porch off of our kitchen and it does block light. How deep is your porch? I live in Wisconsin where sunlight streaming into the house in winter is a good thing, and I personally would not want a screened porch off of my great room if the only windows in the great room looked into the screened porch. I think that putting skylights in the screened porch will help and also painting the ceiling of the screened porch white might help too. Have you considered using big windows instead of screens? If you had windows you would have option of removing the screens in the winter which would brighten it up a bit and keep it cleaner. I have been surprised at how much dirt, pollen and snow gets into our screened porch through the screens.

We found a couple of mission styled fans on Lamps Plus, but the color was not the same as the light fixture, and I guess that begged the question .. which is more important? Style, Color .. We don't need it to match exactly, but we don't want it to be odd either.. Would this fan go with the Light fixture above? Here is a link that might be useful: MIssion Fan

Now that I think about it, he said scissors truss because he was trying to get me a cathedral ceiling while still covering the bottom of the truss with paneling. But as I look at the trusses shown on the link below, a simple King truss would be just fine looking I think. The porch is 13' across and even if you have to include overhangs on each side, we would still be within the 16' that this style supports. Here is a link that might be useful: Truss diagrams

We put track lighting, with dimmer switches, in our 12x16 screen porch, also with a cathedral ceiling. This allowed us to direct light to reading and dining areas and also reflect light off of the ceiling. We've been happy with the result. We also have a ceiling fan, but did not feel the need for a light for the fan. By the way, make sure any fan you get is rated for exterior use, even though it is in a covered area an exterior fan is recommended. Casablanca has a couple of nice ones. Marty