Ah, I was considering the difference between levels would be of only a few tiles of height, but it is a difference of a whole floor, so the viewer is very less likely to be confused distinguishing levels. This part of the map is more than enough to get a feel of it, you don't need to post the whole map. You gave a concrete gray color to the tiles on the stairway which is good. Frankly, this is nice enough, I think it would work even without the forced perspective trick on lower set of stairs. If you are doing it for the lower one, you might as well do it for the upper one also.
Is the map going to be interactive with walking characters and stuff? If so you should consider what happens if the character moves under the stairs (if they are allowed under it). Also, consider making the stairway cast a shadow on the ground.
They way you arranged it, I think it is pretty clear, you can ignore my suggestion of ornate borders etc, and you should keep the north stairs as they are, like eishiya's suggestion. I am not a native speaker also and what said might have come out more complicated than it should
. I like the clear contrast between white walls, red floor, grey stairs and black cross-sections. As you mentioned before, giving a bit of gradient towards a brighter color on the north oriented stairs might make it a bit more tridimensional and bring attention to it, which is good since it leads to another floor and thus it is a point of interest on the map.
Edit: I just noticed a big geometric inconsistency lol, your walls are not tall enough for the stairway to fit as you wanted it to. Pardon my very very dirt edit, it was made from my phone because I had no access to aseprite, also the image was double sized, and I wasn't able to resize to make a cleaner edit. I think it gets the idea across: