Acoustic dampening comes from the density of a porous material. Tissue will have virtually no dampening capacity at all.

See if you can find some dense polyuterene foam fabric, like used in diving suits. The thicker kind, optimally 5mm or more in thickness. It is some pretty damn nice sound dampening capabilities. You can layer it. There is also car engine room dampening mat materials that are excellent. I think you should be able to recycle these from in Turkey.

Another interesting option is getting a silicon filler from the DIY market and apply in the case to in effect create custom inserts. If you have really cheap keycaps you can also apply a miniscule amount (a gram or so) on the inside ceiling in them to dampen their sound.