And so I did that -- to little avail.
Dissapointed, I googled for 'porta pwm 16f628', and I saw that people set something in the CMCON-register, to turn off analog comparators. Intrigued, I opened up the datasheet and googled some more. The solution was simple: set the 7th bit in CMCON to turn off the analog comparators, and the pins will react like normal, well-behaved digital pins.
And now, I have 3 RGB-LEDs changing color via PWM. I'll clean up my code later and post it -- right now it's off to the showers and to bed!