Well I'm thinking of using light steel rafters, to reduce the weight. I was thinking light steel beams for the rafters, joists, purlins and collar ties. But quite frankly I'm not sure what's best. We live in typhoon country, so I'm not sure if light weight is the way to go? I will be getting these to an engineer to go over and approve, but I want to get the layout done so I can finish laying out the rest of the ceiling and roof space, windows, stair locations etc. So as far as a concept design is concerned what would be the best way to lay the beams out for that open space is what I'm after. Also I guess any suggestions, advice, or OMG don't do that help as well :)

I think other are saying to possibly use rectangular "inside" the wall behind this cabinet that is between your kitchen and DR. If that is the case, I do not think that will work or is necessary. 1st you would have to bend/transition to get that into the wall cavity. You want to eliminate bends as much as possible if you can. Not to mention you will have to take a nice chunk out of the back of the cabinet to accomplish this I would think. Not to mention I think you need something like a 5x12 rectangular duct (narrowest) for the same cubic foot of air movement for an 8" round (according to charts I have seen on the web). This will not fit in the wall. If I am looking at the 2nd photo in your attic correctly, you are saying on the right side on the photo, above the electrical junction box, that is mounted on the joist, is where the hole is located. There is another joist behind it that is the attachment point for the DR ceiling Drywall. There is block on top of the joists connecting the two and there also appears to be horizontal blocking between those 2 joists as well. So again not sure anything could be run inside the wall. If the walls are 2x6 then you have a shot. You said you have 6" from the edge of the joist to the front of the cabinet. So you may be able to transition something here within this space. I brought up Oval duct since it has much better/smoother flow, compared to Rectangular. Also, it would be 3 1/2" width and you should have about 3" now, from the front edge of the circle to where the wire was hanging down. Thus, you would only need another 1/2" of cabinet cut to fit the duct towards the front. But the duct would require you cutting wider.

The issue with cutting off part of the bottom of the joists in question is not the increase in deflection at the design load because the old joists are already so stiff and close together that they would far exceed modern code design standards with an inch removed. But because of the excessive sagging, the relevant issue is the condition of the joists and the current loading which we cannot know without inspecting the structure in person. I suspect it would be OK to cut off whatever is needed to level the ceiling and reinforcement would be a hedge against unknown conditions but to be safe (and legal in most jurisdictions) it would be necessary to get the written approval of an engineer who had actually inspected the structure.

I am exhausted. If there are joists up there, I can't find them. I have knocked with my knuckles - and then a hammer wrapped in a towel - for hours on end. Can't find them. I have run my stud finder with a piece of white paper under it over that rough ceiling until I can't do it any more. The light turns off. The light turns green. Run over the same area again and it doesn't do it. Run over it again and it does do it. Then it doesn't. The paper is only 8 1/2 x 11 so frustrating when you get to the edge of the paper. What a hunk of junk. I have hammered finishing nails through the drywall over and over again. Some resistance and then - slips right in. No joist. I've been standing on a 8' ladder working on a 12' rough ceiling for hours. I've got pencil, hammer, rag for over the hammer, stud finder, measuring tape, blue painters tape, drill and bit, extension cord, the hooks - all the tools - I'm giving up. This is apparently just not meant to be. Thanks for your time, everyone.