Electronic – What connector for this cable

I am working on a part of a project for a university exam and it includes an interface with a touch screen.

The touch screen is a classic resistive four wire, it comes with a display of course. Datasheet is here.

We've chosen the TSC2003-Q1 from texas instruments, it basically is a SAR adc that can also drive the resistive sheets, we've made the board and all seems to work but I'm having huge issues connecting the touch panel to the board.

The wire coming from the panel is a sort of FPC, you can see it in this photo:

So I've promptly chosen a ZIF FPC connector from molex, as per next photo:

The problem is that the "wire" coming from the panel is not exactly an FPC: they are usually made of plastic and the contacts are copper or some other metal that is chemically deposited on the plastic substrate, but this is different. The contacts seem to be of graphite or something similar and they're very weak, and here comes the problem. I've been very careful inserting and removing the fpc in the connector but the graphite has been scraped away by the contacts, in the first picture you can see clear spots on the dark grey strips, these are NOT metal strips but is the underlying plastic.

So here comes my question: what connector is suitable for this particular type of wire? Soldering is impossible, the plastic melts and the graphite messes up. Connecting another kind of wire to the screen is impossible too, the resistive sheets are part of the cable itself and the traces seems to be just "painted" with some sort of conductive material, just like the tip of the FPC.