Damn, I don’t know much but we were doing 5/8” taps in blind holes on big printing presses either balancing on a beam or standing on a ladder. Bought a smaller Magnetic drill dress for drilling cast iron overhead. With the mag drill I needed ratcheting tap handle. I didn’t have a spring loaded tap guide right away, just a short piece of 1/2” drill rod I turned a 90 degree point on and followed the tap driver down.
Don’t overthink this, it’s basic. If you can afford a geared head drill press for this job, awesome, get one. I would love one! Total over kill. I bought a Starrett tap handle which I like and I have a guided tap handle for smaller taps. I can’t find a 5/8 tap in my junk which doesn’t have a center point. A pointy piece of steel in the chuck and an adjustable wrench and your golden. While it isn’t an issue to have it, you don’t need a 75% thread form in the hand wheel for a 5/8 - 11 thread. You are presumably not hanging a car off of it?