I'd ask the HOA for an approved window. We sell Sunrise which as has already been mentioned is among the lowest profiles available in a quality vinyl window. I would simply make them aware of this fact and also let them know that what they are doing with this stupid ruling is forcing the entire homeowner group to purchase aluminum windows which aren't the best in terms of energy efficiency.
It sounds to me as if you are the first homeowner who wants to replace their windows and they really don't understand anything about vinyl window profiles. If you have the Sunrise brochure, it shows a comparison to a thick framed vinyl window. I would show that to them and then tell them that rather than you bringing dozens of windows to them that they will surely reject, you want them to come up with an approved window that is also energy efficient and at a reasonable price and that's what you will go with. Tell them you think it's unfair that they are in essence forcing you to purchase a lower energy efficient window and that you will have to live with higher utility bills for many, many years because of their ignorance about windows.
It's worked for me before.