No idea what a spiral point tap is.
The are sometimes called gun taps since they shoot the chips forward and don't require backing out as hand taps do. If you don't reverse a hand tap to break the chip, you can break the tap. I use spiral point taps in a Procunier tapping head under power and all goes smoothly. I am not tapping with the sizes you are though. Check out the spiral point taps, I think you will find them super nice. Use your drill press as a tap guide with a spiral point tap to make a bit easier as well. Not under power though. My Jacobs 16n Chuck has 3/8" Chuck key holes, so a 3/8" piece of stock will allow me to drive the tap by hand and not under power. Hope this helps.