Roofing options for an economical covered deck?

(background: I’m handy, have built a few sheds, and have all of the required tools but never designed or built something this large. We live in SE Michigan so supporting snow load needs to be factored in).

Our house has a 12’x20’ deck and the wife wants it to be covered and screened in. We live in a wooded, wet area so the bugs can be bad and the house isn’t big, so the added living space would be nice. I’m scoping out how to create an enclosed, outdoor space.

The deck has eleven 4x4 posts supporting the railing. These posts were a DIY by the previous owner and built poorly (the railing wobbles). My thought is remove the posts and rails and replace with taller 4x4 posts, bolting them to the deck frame correctly. The bottoms of the posts would be notched and tied to the deck frame. The tops of the posts would also be notched to accommodate 2x6s. The tops of the posts would be tied together by the 2x6s (establishing the proper roof slope). Essentially, the structure would be a freestanding lean-to bolted to the deck. I'm still undecided on the slope of the roof. To maintain a decent amount of headroom, it needs to be relatively flat. I've read that roof structures like this can be 1/4" of rise in 12" of run (1.2 degrees of slope). This is necessary since I don't have a ton of height to play with where it meets the house (88") and I am 74" tall; any more slope and I will spend my time on the deck ducking or hunched over. Trusses within the 2x6 frame would be 2x4s (spacing currently unknown, using 2x4s to increase headroom) on hangers with 1x4 purlIs (spacing unknown) crossing all of the 2x4s. Is there anything overly flawed with this plan for the main structure?

For the roofing, I'm comparing steel roofing versus a polycarbonate option that allows light through. Our largest concern with putting a roof over the deck is blocking light that comes in our sliding door. It is the main source of natural light for the dining room, kitchen, and main area of the house. I'm considering something that is opaque or "frosted" so it is still bright but you are not getting baked. I've read that some of the home improvement box store polycarbonate options are pretty flimsy. Since the roof is such a low slope, I would caulk the seams to prevent leaks. Does anyone have experience with anything that has worked well for them?

Again, I'm not a builder but I am handy. They goal is to get something up that satisfies code (if I were ever questioned) and will get the job done for a few years. We have dreams of something bigger and nicer but the bank account doesn't agree at the moment.

Thanks!

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Roofing options for an economical covered deck?