You could read an analog stick axis on an analog pin and count low reads, say < 300 as one direction and high reads, say > 723, as the other. That's plenty of free dead zone! Then < 100 or > 923 could be 2x as much or some such scheme to get some proportion out of it and have more than an 8-direction hat switch. Still, with time an 8-direction hat switch can work.
I've played with capacitive sensing enough to be 90% sure it could be done that way through the difference between 4 sensors given careful setup. A lot of things could raise or lower the bleed time of all the sensors to some different degree but with work a touch can be a dramatic difference it would be pretty hard to false. OTOH that would amount to a 4-direction hat, or as many directions as you could fit sensors in a ring. You'd have no moving parts and no 80,000 hour leds to wear out.
Maybe it'd be cool to put sensors in the steering wheel and where you hold the wheel would determine the dash light color?