Yes, if measured tight to the opening after the glass has been removed the flush flange would have covered more stucco, and not been even with the existing stucco'd-in frame which is too small.
You might be ready for a long story but that doesn't mean I want to type one.
As I said I cut off those protrusions when I ran into them. And as I said, the plasterers mostly did not keep their plaster surface level with the sides. It kind of flares out especially at the bottom when they are troweling upwards under the window. This holds the window out from the wall as much as the metal.
Unless you are real construction minded and want to do this yourself, good luck finding someone that will fix a screw up is more than difficult. I know, I was that guy.
The cliff notes are that I would remove each window not protected immediately above and install Z-flashing above and over the outside of the fin. To do this I would remove the top section of the frame. I'd still keep the window centered in the opening as it was originally, or maybe lower it a bit if that doesn't look too off from the inside.
The Z-flashing needs to go behind the stucco on the top and stick out far enough that you can slip the fin up under. Running a bit wide will help by trimming the Z. What would I would use might not be available off the rack at the box store. Might even be a tough one at the roofing supply but they do have a lot in all colors. White would be nice.
Water running down the side can usually be managed by caulking the side flanges before pushing the window in, essentially glueing it to the old frame. Then a bead at the edge should double up on the caulking. I did use caulk on the bottom frame in the wall but left the bottom flange edge to wall open for drainage. There should be no need for that if installed properly and I got some criticism for not caulking all four edges. There is still the potential issue of the plaster bell'd out at the bottom. Many times that can be made flat enough with the claws of a junk hammer.
The top is most important as you found out. When I had leaks on these one of 2 things always happened. The caulk at the top shrank and made a little gutter or opened up a bit, or there was a lag bolt for a patio cover above the window allowing water into the wall. People never know about their leaking lag bolts until the window guy shows up and yanks the old window.
Lastly there is a school of thought about removing the old window frame entirely by pulling it inward and not breaking any stucco. Then the window is measured tight to the drywall return. There will be arguments pro and con about that as long as they keep making flush fin retrofit windows.
In conclusion, your windows can be saved but if you remove the rest of the AL frame the windows will have nothing to rest against and fall into the opening. You need blocking anyway, that could work for someone, but not how I'd fix this.
Yes, I I've done a few hundred of these and hated every tract that used that brand of original window. If work was good I wouldn't even give a quote for those houses. In my day I charged $125 per window measured and installed. HD was $165. Don't know what anyone gets today. For a restucco in job my rate was $1000 per opening. That's why these windows exist. Time frame for one man was 6 windows a day, but one day for each stucco back. Patio sliders were 500 and alterations could run into the thousands when new headers were involved. The factories made a 79 1/2" tall unit for just us retrofit guys at no extra up-charge.