Sorry if I'm being a little nitpicky, but I've figured out that this would be impossible on real NES hardware.
1: One limitation of the NES you didn't mention is not just the 16x16 squares, but also there's only 4 palettes total.
for the background, meaning you can only really use 13 colours.
You used 20 colours, 19 not counting the watermark and there's way more than 4 colours per 16x16 square, possibly even exceeding 16 palettes.
2: I'll forgive the boosted palette, but you broke a rule you mentioned already:
'Each 16x16 square can only have 3 colors plus black (or whatever)'
I've found some squares that contain 5 colours, specifically those on the the dress covering the right boob.
But I will give you this. You got me to stare at boobs for 4 hours straight.