I am so sorry you are dealing with this mess, Eam44. How frustrating! I am sure I am not understanding everything happening with this crazy beam/wall of death. But what I hear you saying is that you want to tie the new vent into this old vent and it is causing a major headache. Well, that, and the fact that some idiot took out a load bearing wall and ran off. It is like you have this brand new outfit that you are dying to wear. But, you are desperately trying to make the old shoes go with it. Now someone broke the old shoes heels off. You are trying to get them repaired, but even if you could they really don't match with your new style because they have buckles and you really hate buckles. The buckles are the soffits btw. Ok I think I'm getting way off track with my dumb illustration. Haha! What if you pretend as if that old vent does not exist. Fix the beam without worrying about the vent. I wonder how well it would vent the fumes anyways? Seems like a long stretch to finally get to the outside when it has to make several right turns plus transition from round to a long skinny rectangle. Now without thinking about the old vent, what is the most logical way to vent the new hood to the outside in the shortest path? What is upstairs? If upstairs if no good, could you vent it down instead? ( I'm editing to scrap that last idea because I think that means the dreaded downdraft pop up system which you probably don't want. ) I know you don't want soffits, but if a strait shot up or down won't work, could the dining room side instead have a soffit? Maybe make it look planned by doing a built in hutch or something underneath it? I don't know what the green room is below the dining and to the right of the sunroom, but could it go out the shed roof on the other side of the sunroom wall? Sorry if I'm getting this all confused as I usually do. My comprehension is really bad these days. Here is what I'm picturing for the vent if it cannot go strait up or down. Do I even have the range (red box) in the right spot?

You need a structural engineer. Posts need footings. You’ll need to dig footings. Steel is stronger than glue lam, and smaller. It will not need intermediate support if designed correctly. Steel is always the answer. Along with a work crew that has experience with it. NOT DIYable. Structural work is like racing. How much you want it to be invisible depends on how much money you have. How fast do you want to go? Pony it up. A 300K level remodel is going to bleed it at every opportunity. This is where you need the experienced architect and GC and let them do their jobs.

Wow, just wow! So, no big surprise that if you cut through a support beam it will fail. That could have easily gone in the joist bay instead. You can buy inexpensive steel support jacks to support it temporarily on either side and then build a proper support with a concrete base. And yes, it's a very good bet there's asbestos there in that pipe insulation.

Thank You for the comment it does look like a hack job ..ametuer hour at its finest. Dimesnions are 8ft Height , high side against house. slopes to 7 ft on low side, outside wall. Outside wall spans 8ft in L, width if u may. its a 3/12 pitch roof so its not an issue. Listen im new at this stuff i really like it , i get how things go but sometimes i run into a quandry here and there. This was one of em. The beam size's on the outside wall joist are actually 4x4 posts in concrete. so and also 2x6 as the ledgers, i installed 1. along house 2. middle where new roof meets old. and on the outside wall the 3 4x4 post into cement as outside support so i kinda get the whole support structural idea. Its solid 0 give anywhere. flush, level, squared, its just was rebuilt w used wood not new lumber . so i just wasnt sure if removing those older wall joists is ok. and the window isnt going where ur thinking its going next to door where there isnt a roof butt so. yeah looks like a double a..s..s i understand but im just not as sseasoned on some structural techniques and what bears what load etc sorry but thanks so much for at least responding i really do appreciate it. Heres some pics of a bit better build i just did on a 8x8 shed. thats gotta be better i hope lol. let me know what u think it was my first real build of a substance structure. lol this what i just asked u about and what it was previously as u see lean to attached was just too low and so i thought it be easy to just pop the roof up and on it and extend the roof for head space but just got a little unsure structurly on how far out is ok for this low slope roof.