How to remove a broken Ankylos abutment?

I have a case where an Ankylos Regular C/ abutment non-indexed, is broken into 2 parts which are still held together by the abutment screw. It fractured right at the implant platform. The apical conical part is still stuck inside the implant and the coronal part (with the crown still attached by cement) is freely rotating after I unscrewed the abutment screw. Despite using different retrieval techniques, I was unable to remove it. It looks like the conical part that is still inside the implant is “fused” with the implant due to such a good Morse taper fit of the conical connection. I even used the Kavo Coronoflex crown remover system to try to dislodge this conical part (by grabbing onto the crown) but to no avail. I don’t want to keep using the Coronoflex for fear of breaking the abutment screw, which is the only thing that provides leverage to dislodge the stuck conical part. Any suggestions for how to remove this?