Storm windows are a thing in four season climates, basically just another pane of glass over the existing window in winter. I have known low income people to just staple clear plastic over the frame for the same effect. You might give it a try. Ugly, but better than boarding them up.

Shutters won’t help much. Storm windows are the cheapest help. We just slowly replaced them (exit: the windows with double pain, has filled, vinyl with UV coating) ourselves ($250-300 each at a big box lumber store).

I think shutters (preferably white) would probably help on south and west facing windows. I don't really see them used much down here; the ones I do see are fake. Highly reflective silver tint (applied on the outside) helps more than dark tint. Window awnings would also help. Large trees are the long-term solution :)

Windows are usually towards the end of the list of things to upgrade. What's your insulation situation like? Attic, walls, ductwork? Have you done a leak test to see where conditioned air is escaping? Has your AC been serviced and in good operating order?

I'd check all those out before replacing windows. As other poster suggested. Especially if you have windows that are in good condition otherwise.

FWIW, I’ve heard that if you let vines grow directly on the exterior (or if you run cables and plant the kind of vines that need to climb cable), the vegetation will insulate/shade the house from the extreme sun.

I can’t say it’s 1st-hand knowledge but perhaps worth looking into. Evaporatie cooling might have a small role in that too. Of course the caveat is if you let vines grow directly on the stucco, they will destroy the stucco which many folks consider a bad trade-off. The other caveat is plantlife brings insects so you might not want to bring insects right up to your walls.

I'm using cardboard between the window and screen to block the sun, it has made a huge difference.