In my profession, I have fixed/leveled out many, many floors (some much worse than yours). Dry pack, (3 parts coarse sand/1 part portland) would be the best for your job. Build the level screeds one day (a laser level comes in handy) and do the fill the next day. Use a bonding agent (Lanco works really good) for a strong, permanent bond.

You can feather edge the dry pack as thin as 1/8”-1/4” if you use a good bonding agent. For a nice, durable surface, skim over with a high quality thin-set with portland cement mixed in it.