The 980M works well in the Z1. I don't think you'll get an AMD card to work.
Removing the copper square is not enough - the X-bracket built into the back of the cooler you attach to the card is designed for a NVIDIA card - AMD cards have a slightly larger X so this part won't sit properly.
Also, conisidering NVIDIA designed the entire MXM cooler for HP and the fact I tried an AMD card in the Z1 (with a crappy cooler rigged up) with no luck.