A trip to Home Depot's tool department led me to buy a cheap hand drill model polishing pad set, with polishing compounds.
After using that to polish the flat metal surfaces as best I could, I bent the mirrors to a crude "parabolic" shape, re-polished the surfaces again, washed it with dish soap and water, and sprayed it with clear spray can lacquer.
The lacquer is now drying, so I started assembling the light.
And, this is where I stand with the project for now. After another couple of hours for the lacquer to dry well I will continue the assembly and continue the reporting.