If the concrete is hot, you can move as much air as you want through the inside of the place and all you are going to do is keep moving hot air.....paint the roof with a white paint first....at least that will reflect some heat, won't solve all of your problem, but its a good start......the sprinkler idea is good too.....the solution is to keep the concrete cool....
My thoughts not yours
I have had the same experience for years, the condo I am in at top floor (3rd) has white painted concrete roof, but all 3 sides are also open and exposed to the sun in the afternoon. Once all these concrete top and sides are heated by the sun, there is very little can be done.
The high temperature holds way through the early hours of the morning, my gauge shows cooling only start after 2am (way after the sun has gone).
I have lots of windows and fans, good breeze here on the 3rd floor, but the heat is just radiating from the walls, you can change the air but not the radiation, the window frames also get hot to the touch.
The cool air that comes with the breeze or fans just get hot more effectively than it can cool the hot walls/ceiling.
My next project are the shutters on the outside of windows to close in the afternoon, this way the glass and frame are both blocked. Don't have much hope, but it helps I guess.
I also have a small window A/C for the bedroom that I use occasionally, it tries it's best, but only have success to bring down the humidity, the temperature still stays high - but this is a small one and very low power consumption. I can imagine using a bigger split A/C should do better, but comes at a very high electric cost in such environment (it's more like trying to cool an oven).
My advice is to move, no other easy/cheap and effective solution, penthouses here in the hot countries have a big disadvantage, not worth it !? lol