If this would really be an issue with the model itself, do you believe there would be 790 reported successful makes?
It is almost inevitable that the links will curl up a little during the initial part of the print where they are printed as overhangs. On a well-tuned printer though, this is not a problem because curling will be limited, the nozzle will push down the overhang every time, and the parts will stick well enough that they are not pushed loose.
Your problem is a combination of poor bed adhesion and excessive curling-up of overhanging parts. If you don't fix these problems with your print setup, you'll have problems printing many other models as well.
If you cannot improve your adhesion and reduce the curling by improving cooling, you could work around it by enabling Z-hop such that the nozzle jumps over the curling parts during travel moves.