I'm Doug, and I'm very sorry to hear of your association's situation. My goal is to provide you with excellent service today. I have been a CA licensed attorney for more than 3 decades.
While clearly, someone in the HOA erred when counting the votes, and based on your stated facts there were insufficient votes to allow the renovation to go forward, based on the error a company was contracted with to do the work and contracts were signed.
Despite what the vote tally may have been, the association is legally liable on the contract and whether the work continues or not, the contractor is entitled to be paid for the profit they would have made or they can sue the Association----and they will have a meritorious case in court.
So, given that the work has begun, and contracts signed already, there is little reason not to go through with the renovation because it will have to be paid for by the association whether the association breaches the contract now, or allows the project to go to completion.
You may reply back to me again if you have additional questions, and I will continue to assist you.
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I wish you and yours well in 2017,