I've had two years of playing a guitar (finger-style) using PIMA right-handed. But, when I play with my palms facing towards me, it's natural for me to walk down the strings away from the harp. If I wanted to play chords going up, would I have to turn my palms outward? Or, somehow make my fingers work backwards? If so, that would feel really unnatural.
Yes, you have to make your fingers work backwards from what you're used to on the guitar. While playing the harp is possible with the palms facing outward, it's extremely awkward and the fingers are limited in their motion. I'm not aware of anyone who does it, although I wouldn't be surprised if Harpo Marx tried it out. It's similar to playing the piano with your palms up, but harder.
Another possibility, if you are set on playing the notes upwards from thumb to fourth or little finger, is to turn the harp around front to back. But the way most harps are built makes it awkward to hold them (or stand up to big ones) this way, so it is probably also not worth learning for you, unless you have special reasons for doing so (it's sometimes advantageous for double harps).
I'm afraid, if you want to learn harp, you will simply have to learn the different setup of strings from a guitar. Good luck.