David,
Another thing that may contribute to your problems is using the Scalextric controllers to control the speed of the cars. The controllers are nothing more than a wire wound resistor with a flat metal strip that slides across the wire which varies the drop in voltage seen by the car's motor. When set for a constant speed the controllers will get hot and probably burn the wire on the resistor.
I'm with you on the suitability of the Hornby wall wart! Like you stated they put out 800ma, but that's at the full 15.9 volts. Set at 30% using the Scalextric controllers you're probably getting just barely enough current to the cars to make them go. Like the controllers, the longer they run the warmer they get and I'm sure that power figure is dropping.
So I think a better power supply is an excellent idea. You might try a power supply for a computer. It should put out plenty to run two cars. If you need to vary the voltage to slow the cars down, I would try using a quality 110 volt dimmer switch on the 110 volt side of the power supply. Drop the input to the power supply and you should be able to more effectively drop the power supply's output.
The last thing I would mention is to connect the wiring from the power supply to the track in more than one spot (i.e. if you track running length is 12 feet, have parallel power connections at 6 feet and another at 12 feet). This will more effectively distribute the power evenly.
Hope some of this helps! I'd like to come by and take a look at your project, but unfortunately I'll be tied up until Monday afternoon.
Keep us posted!!! ---------------------------Bill