Hi Lachie,
You did quite a good job with capturing the proportions, that's great. And
your main colors are also quite good - I really have to say I like the contrast of the tones.

The bad thing is that it looks more like a junker than a car fun to drive - which is mostly caused by your wrong use of dither.
In detail I think there are several things to think of if you want to improve the whole sprite.
At first your wheels aren't exact circles, if it's sideview stich with them as circles, at least for the wheel rims (the wheel itself can be a bit squashed)
The other points are: Your sprite has lots of Jaggies, Sel-out, and no AA (or if you'd call some parties AA'd I'd recommend to look up the technique, there was a good tut sheet flying around). The dithering isn't structured and makes no sense and the shading of most of the details is wrong or off. Another huge point is that you dob't give any material information or form wit hyour shading which let's the whole sprite look flat.
I made a gif with some steps to solve some of the problems and added a few own ideas too. I used both of your references.
Let's talk about the process of pimping ya ride:

You'll have to open the gif in your graphics programm to follow the steps in detail.
1 - First I looked at your sprite closely and removed the whole shading, I also worked on the jaggies here and there and tried to remove those I reminded.
I also changed the shape of the bumpers to add a sense of form (it'd be wrong for this perspective but it looks better imo - artistical choice)
2 - I added a main lightsource and a few more details to have a basis to work with
3 - I started with improving/ working on the shading and shaded the bumpers (tried to achieve the metallic material look)
4 - Mostly reflections, I also improved the form of the car roof part and the side details
5 - fixed some proportions and details regarding to the photo and worked on the wheel
6 - made some tonal improvements regarding to the brightness composition and worked on a lot of smaller details
7 - small detail adjustments
8 - I added a cast shadow to giv it depth, although it's a sideview car.
9 - more detail adjustments, shading of the front wheel regarding to the photo reference and added the palette
Now it'd only need some small tweaks regarding to AA, details and clusters, but all in all I'd call it done. Over the whole process I changed and adjusted some colors, but both versions have exactly 15 + bg (transparency) - I don't know if this is a limitation though.
Here is a comparison for a better illustration of the changes:

And here is the pimped sprite of mine as static image:

Try to work on your forms and jaggies and you'll achieve by far better results. Good Luck
