A Vex starter kit will have compatible outputs—though you may have to splice wires to get the proper connector gender. That will let you program it (in a similar manner to the old IFI RCs—they're based on the same architecture). You could probably hack an old joystick to connect to the analogue inputs on the RC, and use a simple variation on the default code to control it.
If you're going to go to that much trouble, though, you could just as easily use the IFI RC you already have (documentation and default code are available
here and
here)—as long you can track down a copy of MPLAB IDE. Actually, if nobody remembers MPLAB, there is probably an easyC default code for it that will work with the
trial version of easyC PRO from Intellitek.
Alternatively, most other R/C car receivers will generate the right signals, but you'll have to control it with an appropriate R/C transmitter (e.g. with thumbsticks or a wheel).
If you're dead-set on building your own system, consider the ST Micro
STM8S-Discovery evaluation board. (Free samples available from ST Micro, or cheaply from major distributors.) You can configure it with one of the standard examples to generate PWMs...but I haven't tested this myself, so I don't know if there are any practical limitations. You'll need to plan ahead, because the compilers (Cosmic, for instance) need registration codes that will take a business day or so to acquire (free, via e-mail; instructions on ST's website). More information
here.