Will replacing windows significantly reduce solar heat gain in summer?
Different types of solar coatings (and where they are installed on the glass panes) can make a significant difference in the amount of solar gain.
There are various types of solar coatings and each serves a separate purpose. However, they all allow vision out the glass.
You indicate some of the double pane windows have failed. I’d take this opportunity to replace the glazing units with special solar coating. Here’s an article that explains the various types:
https://www.google.com/amp/glassed.vitroglazings.com/topics/how-low-e-glass-works%3Fhs_amp%3Dtrue
In addition to the various types of solar coatings, there are 4 surfaces to a double pane window where the coatings can be applied. Installing it on the inside surface of the exterior pane will provide best reflection.
This process needs to be accomplished by a window manufacturer, but you do not need to remove the window frame, just the glazing.
I’d do all the panes so all the windows look the same when viewed from the outside and inside.