How best to cut & tie into cast iron pipe
I would consider cutting the whole mess out at the bottom end and connect A new “ABS”  black pipe with a “no hub”
 it is a rubber connector with bands on each end to tighten then tie into the upper area .
This will be much easier than packing oakum and poring the lead on top;  everything can be fitted together prior to gluing so you know it is right where you want it then glue and know u fixed the mess.