My experience with PBW and soaking the roti basket and grates was everything just wiped off with a sponge - zero elbow grease. Which is great, given all those nooks and crannies in there. I also find that 4 - 8 hours is plenty of soaking time.
As far as I know, there's no safety issue with mixing them. It might be the best of both worlds, because with PBW, if there's a lot of grease, a film forms on the surface of the water, which the Dawn might break up. Not a major issue, since you have to rinse everything off anyway. It's just that your hands get slimy/greasy reaching in to pull the grates out.
I'll look around for oxyclean with the green lid (no fragrance?) and give that a whirl.