Four jaw and clock is probably the best option with inevitably limited home shop facilities. Mounting needs a bit of thought to get a clean grip on the drill, especially with a large drill in relatively small chuck jaws. May well be worth making some pads to extend the jaws a bit so all are cleanly on the flutes. But that isn't as easy as it sounds. Probably some form of location needed to ensure they don't tilt.
I've got loads of kit and better ways but with limited equipment would probably make an alloy sleeve with a single slit in it to compress down and grip the smallest drill then bore it out for each successive drill size. Need to fill the slit for each bore out of course.
Rough turning is due to Bubba thinking its an easy job and just grabbing in the three jaw. Inelegant, unbalanced, partial gripping on the flutes meant it was unstable.
Coming to the conclusion that every time you think "Ha, nice easy job." you should walk way, get thinking cap and cuppa then sit down and properly think it through. I pretty much never have issues with the obviously harder work that clearly needs thought. Its the "clearly obviously easy" stuff that has the gremlins sharpening claws and fangs in anticipation.
Clive.