Right, 3 colors per 8x8 tile is an NES limitation, but this is limitation for objects. However they have another, more crucial limitation, which is at most 8 objects per scanline. Samus' ship would almost certainly be handled by background tiles, whose color limitation is in fact 3 colors per 16x16 area. And there can be at most 4 of such 3 color sets at once.
To make your ship more accurate, you could paste it on black background and remove one color. To do so, you may experiment for a color, that would shade both the hull and the engines equally well.
The windshield can be on the object layer. Currently, the green area alone takes 36x17 pixel space. Try to compact it to 32x16 (which takes 4 tiles along with mirroring), and maybe share its palette with Samus. You could even draw the cabin of the ship as an easter egg similar to TMNT3 intro.
But overall, the graphic itself looks good. Laymen probably wouldn't appreciate the extra work, but hardware limitation enthusiast would certainly do. The choice is yours.