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Hi Ginnie,
Perhaps you could talk to your city or county government about this parking issue. You can try requesting an ordinance like we did, though this required us to coordinate with a city representative and fire marshal. We also needed to put up signs that said “no parking” every few hundred feet or so. This created a different problem with aesthetic and yard maintenance but we eventually resolved those as well.
In our case, since it is a city ordinance, our HOA can’t enforce the rule per se. The city enforces the restriction and issues the tickets. But if your HOA’s aim is to prevent congestion and abandoned vehicles, then requesting help from the city should be able to take care of that.
Sure hope this helps with your situation.