Another Roof Framming Question

dproc

I guess it's screen porch season. I have another framing issue. Customer wants a 16 x 20 screen room with closed ceiling. I have a couple issues. House is L shaped where porch would go. A-frame or shed roof?

For shed roof:

Second floor bottom window height is 12' from FF- I may be able to get 4-6" by stepping down from FF of house. @ 16' out 3/12 pitch w/ 2x12's I put top of frame at 12'-10" @14'out I gain only 6" . Even with drop in floor it wont work. I don't think 2x10 make a difference. I don't want to go flatter than 3/12 customer wants to use matching shingles. I was thinking of using TGI's for rafters if I can get narrower, shorten porch to 14' and drop down.

Any suggestions for rafter size/product?

For A frame:

Plenty of height between windows but porch tucks into corner. House bumps out 12' requiring a cricket 12' long. Customer worried about leaking. At first I was leaning towards shed roof but height is to tight. If flashed properly I don't think A-frame would be a problem. House is covered in vinyl. Am I right in thinking cricket should not come to a point at vinyl outside corner? Have valley of cricket 8-10" higher and close in triangular area (vertical wall) with flashing. So many things come together at one point.

Framer33884

man that is too much too read, would a super gutter work? I really didn't read it.