Well you have all given me plenty to investigate and think on. Hopefully I can just google these things and get some specifics. My best move now is to post some pics to clarify everything. Expect them in the next few days.
oldog > The 1/12 pitch. Ya, I figured that was a bit on the flat side. The gutter collects quite a bit of water when it rains. Maybe not enough or fast enough. Not putting clay tile on this roof. Rafters won't hold the weight. Asphalt shingles as it has now or possibly metal are my current choices. Do you have a brand of this high temp peel and stick water barrier you mentioned? Something I can google. This Adventac sounds interesting. Is it overkill if I use shingles?
joecaption > Sag on 20 ft rafters. Good point. That's something I'll have to check. I'd imagine a string pulled tight along the bottom will tell me how much of a sag there is. I would guess the only remedy would be replacing with 2x8 or 10s.
> Sky lights. The adjoining kitchen would be a morgue without them so they are a must have. One has been leaking from day one.
> Drip cap? Yes, on the gutter end, not on the exposed slope side. The patio roof is attached to the house on two sides.
> 3 tab shingles? Not sure what that is but I'll look into it. EPDM. Now there's something to google.White? I've thought on that. I'm sure it would work great but there's the aesthetics. Still considering.
> Metal roofing. Spent some time researching it. There's plenty of different types. One common theme seems to be it's a good bit more of a challenge to install, more expensive but lasts forever. Sure like the "lasts forever" bit.
> Cover the underside. It's not something I considered when first looking into this. Like everyone else I'm trying to hold the cost down. That would about double it. Not ruling it out though. I'll look into all of those. Agreed on the paneling. Not on my patio. Wonder if there's a spray coating (not paint) of some sort that would hide everything?
I'm going to be busy installing a back splash, lights and lots of trim work at my daughters house the next couple of weeks. I'll wiggle in posting some pics. Thanks again.