I am finishing my garage and I have come to the point I need to start drywalling. I ran into a roadblock and would like to get opinions on how to proceed. The roof is a pyramid shaped hip roof and each rafter has a small "notch" where it meets the top plate. It hangs down far enough that it would either require notching out the drywall on the ceiling and wall where they meet. This sounds like a big pain. I was wondering if it would affect the structural integrity by cutting the notch off so that I can get it flush with the ceiling joists, or if there is an easier alternative to notching the drywall. I have circled the "notch" in several photos below that I am referring too.
You would lose a bit of strength. I would recommend checking to ensure all rafters are secured to the top plate and to the horizontal members spanning the proposed ceiling. Given the snow load you would experience in Chicago (if you profile is correct), you need more nails and, I would recommend, ties if you try to go that route, but I do not recommend it.
I recommend furring the ceiling with 2x2s (or 2x3 laid flat for extra room to screw into) on the horizontal members and attaching the ceiling to that. You lose 1.5" of head height.
If that is a problem. Stain/paint the birdsmouth and drywall around it; that would make a nice visual in my opinion.
Do not remove those. That small bit of wood prevents horizontal sliding of the roof beams, and therefore roof collapse. Those two screws that attach the horizontal beam can't compensate for that if you remove them. Roofs have to deal with dynamic loads (rain, snow, wind) and under those situations they'll need to be able to carry off extra weight.
This is your current situation:
Removing those will have this effect:
Imagine standing over a wide crevice with one foot on each side, flat on the ground. Your feet want to go further sideways, and eventually you'll fall. Now imagine resting your feet against the edges of the crevice. That's far more stable.
It isn't a big pain. You plasterboard up the walls to the bottom of the bits you want to cut off (Don't). You plasterboard the ceiling till you reach the same bits. You put strips along that slanting line rather like coving would go. Not much more, if any, cutting to do at the end of it all. And, it'll look quite classy!
Those bits are an integral part of roof strength, better than the nails that hold it all together, so shouldn't be removed. Don't forget all the insulation bats.