Well I think I addressed some problems:
The top one is my original, but I think I fixed the inside, or at least tried to. I'm not very good with progressive darkness with limited colors without making it look like a gradient.
The bottom one is my attempt to fix the perspective issue. Though admittedly I think I was trying to go for some sort of perspective on it, along with the shape... but very subtle. At least subtle enough to the point the perspective wouldn't have a dramatic outcome on the lid.
