I think we should consider that Harry Potter was written from the beginning to the end, in the way that apart from the idea of Harry confronting Voldemort, JK didn´t have anything planned that far ahead when writting. So, in my opinion, up till book 6 his was just another invisibility cloak. If it were a hollow since book 1, probably Dumbledore would have discovered way sooner that if cloaks got wasted after a few years James' was special, Ron would have mentioned it, or hinted in a way, so we later could find out and think oh gos, that was why. And yes, Moody´s eye wouldnt be able to see through it.

About paint. physical explanation would be the cloak bends light around it as if nothing was there, or more humanly, displays in one end what records in the other. But still it covers something solid, so either painting would stay on top of the cloak targeting it, or it would disappear.

 

I think that the master of death was always meant to be a pervelle descendant. It can't just be happenstance, that in the story it specificly referees to how the cloak was passed down the family line. I can't but wonder if blood magic was used in the creation or use of the items.