Will they throw a fit if you remove the shutters? They are not appropriate for double windows and so are dubbed "faux stick-on shudders." Read through the HOA rules and see if you can take them off. Then tackle the landscaping so as to "knock their socks off!" Forget about painting the garage doors. If they have a top row of panels that can be removed to reveal glass windows, do that. Otherwise, consider changing the doors to a style that has windows up top.

Neither. Don’t paint then to make them stand out. Garage doors aren’t a design feature.

pick the very dark gray the HOA will allow.... if it wont void the warranty of course

I think your roof is gray, so might try a gray. Also, if you can’t replace garage doors so you have windows there are magnetic faux window products that might be worth trying. Here is mock up. Hard to do tiny windows in this mock up but might help you visualize.

Here is magnetic window product.

What an interesting window product! Might be just what I need!

White balances out your house, so I would leave them white.

I voted black if that is your only option but if it were me I would paint the garage as close to the brick as possible so it blends in rather than being a visual focal

We have similar brick colors, my house used to have white plastic shutters. I replaced them with wood, stained dark brown and then painted my garage doors similar to the shutter's color. I like the end result. Better than what it was when I moved in.