Their is cumulative error of each part in a chain, and there are other issues like separating the adapter. Make sure the adapter is tanged, otherwise it can get jammed in the tailstock. I use a MT2 to MT3 adapter for me smaller MT2 drills in the tailstock, they have a small side window for a wedge to pop out the MT2 drill. It may take some time to break in, but that it got so hot means it is still very tight. There also might be other options like turning down a portion of the end of you rod to dimension, then sliding a metal cap on the end that will be used up against the center or some other form of interface. The Skoda I have has interchangeable tips so sometimes I will use a flat other times the small point.