boring through the tailstock

this is how I long hole bore for my lamps, boring half way then end for ending the timber! there is other ways but this works for me I still have and use a hollow dead Centre but it had a tendency to burn the end on softer timber despite waxing, oiling etc.
after boring one end I swap centres in the headstock to a home made one that locates the hole on Centre. I guess you could rough turn the blank and use a chuck to hold it as well.
I also slow the lathe down and speed is dependant on the Timber shape, e.g the fence post lamps are out of balance so starting speed is 100 to 500 rpm assessing vibration where as timber that is a cylinder I would double the speed.

You're using a commercially made auger?

It looks to be sharpened differently to mine, which is basically just an old hand auger which I resharpened to a centre-point type bit.

the one in the tailstock is a brand new P&N. the other one's I have are round bar with a twist drill bit welded to the end!