Here is my take:
First off , that machine (i am guessing) has a spindle reverse and the feed is via separate drive motor (DC) ...if this is true
then you don't need a tapping head...You can just reverse the spindle and back the tap out....
Might be faster to use a tapping head, but they use up valuable head room that is in short supply on the FP1.....
If you wish to tap using the Z and power feed, then you must use a compression.extension tap holder.
The depth a tap goes is a function of the tap pitch and the exact RPM that the spindle is rotating...Depth then becomes a time function over the speed as the tap makes its own depth (time/speed)
Easiest is just use a rigid tap holder or collet in the vertical spindle and run the tap down using the quill....when it hits depth, reverse the spindle and back it out....
If tapping blind holes. there are friction overload drivers that will release at a settable torque., can run them down till they hit bottom and hopefully the drive will release...Me , i just mark the depth with a sharpie on the tap, a bit short of the depth needed. Run it in till the line is reached...
Using a tap driver with "Bliz" style collets, I just uncouple the tap and allow the quill to raise up out of the way, then finish to final using a tap handle....
Takes a bit of time , but way less than removing a broken tap....
Cheers Ross