Thanks to everyone for the comments and suggestions. I'll be working on this in the coming weeks, I'll post updates when I can.
My goal isn't to make a perfect clone of GTA, there's just way too much in that game to squeeze in to 32k.

I just had that game in my head when I started working on this. There's not going to be enough space to create a mission based game like the original, I'm going to need to have a single, basic "mission" or goal to beat the game.
A few thoughts on the comments...

Mission dialogue could be presented in silent film format (in their own screen)
I like that idea but I don't think I'll be able to do it due to space constraints. I won't rule it out until I play around with the idea a bit, though.

Cars could be represented by playfield pixels until stolen by the player.
It wouldn't be hard to do that, I could have randomly placed parked cars that could be stolen. I could have faster/slower cars, and maye alter how they handle a little bit (like the "ice" track in Indy500 for a poor handling car, for example). I'm not sure if changing cars would make much difference in gameplay other than making it easier (or harder) to get around on the map, though.

For that matter, pedestrians could be playfield pixels.
True enough. I'm going to have to be creative with how I use the ball, missiles, and one extra sprite. The sprite will either be used for other cars on the road or pedestrians, but one of them is going to have to be a ball or missile.

I thought there was a life counter mini kernel. You could use that for stars (wanted levels) instead.
There is, and I've already got that incorporated into the game. I could use a 1-3 three star wanted level rating on one side and a health meter for your car on the other. I'm not sure what I'd do in the game once you had a higher wanted level though, being chased down by dozens of cops isn't going to work.

If you hack yourself a 16 character score kernel you could use it for current weapon and ammo.
I could incorporate limited ammo and a counter to keep track of it, but I probably won't be able to include multiple types of weapons in the game. Of course, just changing the firing rate could make a pistol into a machine gun, right?

I still think
THIS could be used for a scrolling map screen if it could be updated for the latest bB builds.
I remember that, it's very cool. Using and modifying that code for this project is a bit beyond my skill level, though.

But in this case one player at a time would speed through the streets of a post-apocalyptic world, running over various types of random pedestrians for points and picking up bonus items that randomly litter the roadways

In your version, there could be crusty-looking pedestrians that should be avoided since they carry bombs that will damage your car if you ram into them.
I had thought about doing something like that. There needs to be something on each screen to either avoid or try to kill. I like the idea of pedestrians that could be taken out for bonus items or points.

would it be possible to change exiting your car from the console switches to something on the controller, or second controller?
Yep, that's an easy change, it will probably be changed to the second joystick eventually. For now, I'm going to leave it like it is - it's easier for me to keep it that way for using it with Stella. Using the touch pad controller would be kind of cool too, I think I saw a thread that demonstrates how to do that.
I've got lots of work to do! Thanks again to everyone for all the ideas, it's definitely got me thinking.
Steve