Here are pictures of the areas I think are important. I don't have a good picture of the entire porch from the yard, but the roof has a gable on the front which we recently had covered in vinyl shakes. The current drink rail is very wide (7"), at the thinnest edge by the door it is 5.25".

Thanks all! Agree @Woody Vaughan or Shaun Fogarty on the too many skylights problem with the shed roof. One question I have is whether we could do fewer but larger skylights. @Seabornman I like the idea of cleaner install and exposed rafters! @Patricia Colwell I understand the risks of darker living spaces - the back of the house faces south and is very very sunny. Our architect has reassured me that the skylights would make a big difference in maintaining good light internally. Here are a side elevation for each option - not sure there's much difference there. I should note in all of this that resale isn't an issue, also that we are in a high-cost area, but even post-reno our house will be one of the least expensive in the zip code. Which means we can't over-improve but also that the next owners (in 10-15+yrs) may well knock the whole thing down (as occasionally I think we should have!)

I would like to extend my small screened-in porch into the deck area to create a covered L-shaped screened porch, but I don't see an easy way to add a roof over the deck that would tie into the existing roof lines. Any thoughts or ideas?

Your roof framing is missing structural elements, so the roof loads are pushing your walls out. Google "rafter ties" (you have "collar ties" what you are calling "cross beams", and those are fairly insignificant compared to rafter ties). You can still have an open ceiling with a finished surface plane though, you just need some lower "cross beams."