The joys of home ownership :) You don't have to tear up the stucco. Here is a good method. Get a diamond blade for your circular saw. Get an expensive high quality one. On the outside, right NEXT to the exposed aluminum frame, cut through the stucco AND the nailing fin. Experiment with your blade depth because you don't want to be cutting into the stud. Diamond blades don't work so well on wood! Be careful on the corners to get a full cut - you'll have to go past 3/4" to compensate for the circular shape of the blade. When your finished, the old window will lift out if it doesn't fall out, so don't hold on to the window when your cutting. Also wear a mask because this is very dusty. At this point, you should end up with a clean cut in the stucco. You should measure your window to be app that size, and you can do that before cutting. Give yourself a minimum of an extra 1/4 inch all the way around for easy fitment between the stucco. You will most likely be behind the sheetrock at that point, but that's not for sure. Once you do one, you'll know how to do the others better. Worse case, you'll have to cut the stucco twice on the first one. DO NOT forget to flash/drip cap above the new window. You can get up in there with a sawzall blade and cut the nails to remove the upper fin, which should give you plenty of clearance for your drip cap. Go ahead and rip out your sheetrock before installing the new window, and then just jamb up to it once it's determined where it will sit. You won't loose much glass area, if any, if you do it this way. The new window, in this situation, will stick out past the stucco app 3/8 of an inch. You will be able, hopefully, to put a nice neat bead of caulk around it that way, with no raw stucco edge showing. Be sure that you measure for this from the inside surface of the wall around the window all the way around, because stucco can be much much more uneven than the inside sheetrock. Don't forget you can measure where the studs are by measuring between the sheetrock on the inside and adding for the thickness of the sheetrock. Compare this measurement with what you get measuring the exposed aluminum frame on the outside - BUT, use your inside stud to stud measurements for your basis of determining the new window size. Also, do not forget, window sizes are always width first. width x height. Always. If this sounds like too much for you, bit the bullet and have the pros do it. If you don't know what you're doing it's not hard to butcher this kind of job. Worse worse case, you're patching stucco, but that will always have a tendency to crack where you patched it. And please be careful with power tools on ladders. Always have a helper or two. Preferably one to steady the ladder, and one to hold the window. Tie off the ladder, tie off yourself. I hope this makes sense to you. Good luck.

Milgard Ultra Series is a fiberglass window with a black exterior and interior frame. https://www.milgard.com/windows/ultra-series

Are you saying that you want to install replacement windows - pull the original windows and install new ones - or are you saying that you want to keep the original window and install a second window over the original? Also, tempered glass does nothing to improve sound blocking of a window, but thicker glass might depending on how it's done.

What is the climate like there? If it's not too cold, thermally broken aluminum would still work.