Minimum wire size permissible?

MarkT:
I think the power transmission ratings are assuming lots of wires bundled in the same
conduit without ventilation, so are more conservative.

The official rating charts are very conservative. They assume thick bundles of wires in places where heat can't escape.

OTOH it's a consumer product, better safe than sorry.

A good way to tell if you need thicker wire is to look at the voltage drop along it. If it's more than a few percent then you might need thicker wire.