Scared by the arm-breaking torque warning for the 3-gear reduction B&D drill, I bought a 2-gear reduction drill I found on craigslist, though I already bought a 3-gear reduction Milwaukee drill. This no name brand has 1/2" 3.5A 500 rpm single speed no reverse, 60's drill according to a youtube video. I hope this can push 1" auger into a tree stump with ease. If this doesn't work, I will have to use the 3-gear reduction Milwaukee.
Thank you all for your advice. For your amusement, I am attaching 3 photos. I opened the drill to add lubrication and found no ball or needle bearing, just bronze sleeves, definitely a home use drill. The tag is not even riveted, held between 2 halves of the shell. Side handle is a 6" long 5/16"-18 bolt from AceHardware. Thank you.
I assume that you're using an auger paddle bit with a central cutting tip, like a needle, almost? Start your stump hole w/the 1" bit, just to-cut down into the stump maybe <1", then switch to something smaller, like 1/2", 5/8", or 3/4". Use that to bore your hole as-deep as you need, then switch-back to the 1" paddle bit. Already having the 1" shallow hole there will keep the 1" bit in the hole, having removed a lot of material with the smaller bits will make the 1" cut easier. If you used the smaller bits, and then tried to use the 1" bit, your bit will wobble like a drunk at midnight.
I suggest using a piece of 1/2" or 3/4" (if you have bigger hands than POTUS) PVC or poly-pipe on that hex bolt, to give you something more-substantial to hold. If you really wanted to get schmancy, you could use something like caulk, epoxy or adhesive between the bolt and the inside dimension of the pipe. Depending on how-much effort/time you wanted to put into it, you could use a wood dowel w/a hole drilled through it. Slip that into the pipe. You can make them in 1" segments (that would make drilling that central hole easier and more-accurate) and stack 'em inside the PVC/poly-pipe, on the bolt. Drill the dowel hole just big-enough to snugly-fit over the bolt. Use a flat washer on the hex-end of the bolt, to tension the length of the pipe against the body of the drill. If you believed there was some benefit to having a rotating handle, then leave the pvc/poly-pipe a hair-shorter (your choice of hair color, red, brown, or blonde) than the inside distance of the hex-head to drill body measurement.