>>435895A lighter and more compact option would be one of these. I own a collection of old carpentry tools, because that shit fascinates me, and I'm often amazed by how effective they are. These particular bits really caught me by surprise. They cut surprisingly fast and extremely clean. They work very much by the same principle as a modern auger bit, in that they have one blade that slices a circle, and then a chisel that lifts out the waste, only it doesn't have a guide screw to force it into the wood and no Arkimedes screw to lift out the shavings. This means that you have to pull it out occasionally to remove shavings, but the lack of a guide screw means you don't have to "unscrew" the drill bit to do this. I also suspect that the unforced progress explains the cleanness of the cut.
I've only tried them with a brace type hand drill, could be that a cross handle like you have would make for a slow drilling, but if you can find a drill bit like this at an antiques shop, pick up a couple, shouldn't be more than a couple of dollars a piece, or you're being ripped off.
Come to think of it, I'll give it a go myself when I get around to it, probably tomorrow.