We don't know the distance from the 4x12 beam over to the next support. So, we don't know the load (tributary load in pounds per linear foot) on the 4x12 and therefore we don't know how much, if any, the 4x12 can be notched.
However, assuming you have calculated the Total Load (LL + DL) correctly at 90 psf, then a No. 1 Doug. Fir 2x8 at 24" o.c. with a load of 90 lbs. per square foot (180 plf) can span a maximum of 9'-0" with a bending stress of fb = 1500 and modulus of elasticity = 1.4. If you need the 2x8 joist to span further, you could span 11'-0" at 16" o.c. Or span 12'-0" at 12" o.c. (This does not account for "short duration loading" (snow that lasts less than 30 days) or "impact loading" (snow that lasts less than 7 days) like where I live.
Therefore, to determine if the 4x12 beam is adequate, I calculated the maximum tributary load on the 4x12, which is half the 9' span plus the 2' overhang, which is:
4.5' + 2' = 6.5' x 90 psf = 585 plf
The maximum load on a 4x12 spanning 10' is about 700 plf (Therefore, the 4x12 is slightly over sized and can be notched...if the 2x8's only span 9', which I'm guessing they are over stressed.)
So, I think there are 3 options:
Option 1: The 2x8 joists are in "reverse-bending" as they pass over the 4x12 beam. So, the top half of the joist is in tension and the bottom half is in compression. If you carefully notch the bottom one-third of each 2x8 so that the joist fits tight over the 4x12, then the overhang won't sag or fail.
Option 2: if you lower the 4x12 enough to let the 2x8 joists to sit on the 4x12, there would be no need to notch the joists.
Option 3: The 4x12 is slightly over designed, you could notch the 4x12 beam a maximum of 2" (making the beam an equivalent of a 4x10).
Note: In your original statement you indicated that the total load is 90 psf. This seems extremely high. Did you mean 90 plf on the 2x8 joists. If so, that would make the snow load 40 psf, which is high, but reasonable. (Meanwhile, I'd double check the span of those 2x8's.)
Best Answer
With the "cable system", there are metal rods in the frame between windows that go the full height of the window and are tied into the frame. You connect a cable to an eye at the top of the window and run it back at an angle to the wall the window is installed in, above the window. The other end of the cable is fastened to a bolt that is securely fastened to the framing of the wall (this may be a lag bolt or a through bolt, depending on how the wall is framed).
I don't think these windows have this feature however. If you go to Support > Installation Instructions for the windows you posted, you'll see this quote (emphasis mine):
So if these are the windows you're getting, it looks like you're stuck with the support under the bottom.