As others have noted, the voltage drop is almost certainly the issue. However, the recent rebuild adds a wrinkle.
In order to narrow down the source of the problem, I would measure the voltage at the battery and then at the windlass posts, under load, to determine the actual drop, but based on this reading alone, at the switch, it's significant. For motor loads I shoot for 3% and I can easily argue that a windlass is a critical component, so it falls under the ABYC 3% guideline.
I would not install a bow, windlass battery bank to "fix" this problem. Doing so requires meeting a host of ABYC standards, including security (much more movement and G force in the bow) ventilation and over-current protection, not to mention charging. I don't like the idea of sleeping on batteries too. I'd also want to be certain the problem is voltage related before adding batteries.
In my experience it's almost always simpler and cheaper to supply power to the windlass with the right cabling.
Why was the windlass rebuilt, was it malfunctioning?