BTW, do you have any clue about why it skips 28? Could it be something wrong with my math?
No, not really, except from the fact that you only get two counts per degree from the ADC. You might wan't to try taking 10 or more samples and average them to filter the signal. Also it's possible that you're running into some kind of rounding error in the math due the low resolution but I haven't looked into it that much.

Regarding the external Vref I'd suggest you look at the datasheet for the particular PIC you're using regarding the ADC and its various Vref options.

Another option might be to just put an OPAMP after the sensor, boosting the signal by a factor of xx to better utilize the full range of the ADC.