Oh nice, I like the direction you moved in.
I started this edit the other day before realising you wanted to work with a really restricted palette:
Regardless, the concepts I applied I feel are still very relevant. They are:
- Priority. Sprites should take visual priority over backgrounds. Lowering the contrast and colour dynamic of your backgrounds and increasing them in your sprites helps this.
- Interest. Your player will be looking at the player sprite a lot, so it should be interesting to look at. Rounding out the form with stronger lighting, adding interesting colours and just boosting detail in general are all positive things for a sprite.
If you want to translate these concepts over to an extremely limitted palette, you'll have to make a few sacrifices, most likely to detail. But it's better to have a lower detail, but colourful sprite, and lower detail but correctly-prioritised background than it is to not have those things but have lots of detail across all elements.
What I mean is, have nice colourful colours in the palette JUST for sprites, and then lower-key ones for backgrounds that may also find some roles in the sprites. This will mean you have less total colours available for the background (resulting in less tools to render detail with), but you will have much more functional graphics.
I hope that makes sense...