don't know how the HOA's come up with these "rules". Did anyone go to Rhode Island School of Design (or the like)? This is Kylie's design (and my suggestion):

This paint color could be B.M. Classic Gray OC 23, an off-white color.

I have a similar color house and similar color roof. I love your inspiration photo! Are you changing the color of your roof? Its much darker than your own roof.

Can you appeal your HOA? Do they have colors that are as close as possible to white or very light?

Maybe you can show your HOA some images of white houses and maybe they will see your perspective

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this color is more creamy

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Are you not fond of the trim detail around the windows… etc.
I’m assuming the difference needs to be the trim along the roofline…

So you can paint the body white and the trim/ ornamental designs around the windows etc and the trim along the roofline that Bronzey color like your inspiration.

I would paint all the white dove and have a back up plan IF trim needs to be highlighted and minimize that effort where it makes sense aesthetically.

I think it is a good idea, as you said what’s the worst that can happen ?

How much of a “difference” is required? They can both be white in different shades.

IMO this white-on-white combination is stellar. I've been saving this photo for a long time