Wolfie,
To answer your question.
The normal way to cut a thread to the bottom of a blind hole is to use the second cut tap of your tapping set, thread as far as you possibly can down the hole.
With the plug or bottoming tap, very gently grind the end off completely square, making sure you don’t over heat the tap by continually quenching it in water. You grind off all the lead in taper and point, if it has them. Carefully deburr all ground edges. I use a small diamond file for finishing mine off, but try not to touch the main cutting edges of the tap.
Then by feeding down the previously tapped second cut hole, using plenty of good quality cutting lube, you should be able to finish the threading right to the bottom of the hole. You might have to retract the tap fully a couple of times to clear out swarf at the bottom of the hole before getting to final and full depth.
As you have said, normally supplied taps won’t cut all the way to the bottom, but by doing what I have suggested, will get you as far as possible by hand tapping.
Bogs