hi mlinkadesol
hammer it a bit, just like shown in image 1, maybe a bit of play will be created
considering that the hexagon of the screw is in good condition, take an allen key, kick it with the hammer, and when the hammer is touching that allen key, right in that moment, try to rotate it : this procedure requires 2 people : one will hold the hammer and kick with it, and the other should rotate the key when the hammer is at full force of impact : those 2 persons must work in syncronization, unless you can do it alone
this is showed in image 2, left side; my advice would be to use a "custom T-shape allen key", with a disc wellded on side, so to have a bigger contact area for the hammer (n image 2, right side ), and also use a strong long pipe, that should fit the allen key; the "key" for this to work is the sync action, thus rotatting the pipe+allen key, exactly when the hammer is kicking; also, a good quality allen key is required, not those cheap ones, that get wear imediatly
if hexagon of screw is not in good condition, then try to weld the key inside the screw; carefull, i am not an expert about welding on cnc's, so maybe is not a good idea
also, the hydraulic cilinder should be somewhere at the middle position, thus you need to be sure that it is not creating tension inside the collet chuck; so far i have not used collet chucks like yours, and i don't know exactly what parts are there, but, in any case, you should avoid having pressure inside it from the hidraulic cilinder; you may push the foot pedal to start moving it, and push emergency stop when it is somewhere near the middle
one last resort is also a portable edm, but since you are on a cnc, try to use the live tool, so to drill / mill the entire screw out; if you have live tooling, give it a try / kindly