I believe I can summarize the responses to my question, "Are there better tools for drilling tiny holes", as "Yes, there are many better tools, and everyone has their own favorite. Most seem to prefer HSS (high speed steel) bits with manual drills/pin vices, though a few use powered tools, at least in some cases. For example, per @wefalck, 'if you can put the part under a (quality) drill-press and hold it safely, this may be a good option for even the smallest drills. Otherwise, use a pin-vise or similar'".