Laying Stone on a unlevel concrete surface
I like it and it should get rid of that trip hazard door threshold. I'd stay away from the self-leveling anything and you don't want nor should now have level anyway. As you said, you just want to bring the dips up.

Self-leveling concrete/cement would destroy the porch's pitch for water to run away from the house. You just want Flat, which is not the same thing as level...like a stairway handrail is flat, but not level.

Also, new cement doesn't really stick to old with much strength, so either way, you'll need Bonding Agent if you plan on a full-bed mortar job. Since, you don't want things shifting and you don't want people sliding off an edge of loose stone. Yep, I've been to quite a few places that just laid stuff naked or on a sand bed.

I'd go with Type-S mortar and just back buttering for the deep areas, as it's hard as the stone and much better at standing up to weather. Type-N is what a lot of people use, but I've found it to crack easily and even crumble back to a sand quite quickly at a number of places I've visited.