The old saw about Irwin-pattern bits not working in hardwood is definitely not true. I don't know about exotics, but I've drilled many holes in white oak, beech, and other domestic hardwoods with my old Irwin augurs, no problem. I would check to make sure the bit is sharpened well.
Personally, I love using a brace, and I get cleaner, straighter, more accurate holes than with an electric drill. I definitely encourage you to keep at it!