The sharpest bits I have used have a 30 degree included angle and .005 tip. Again in wood with no breakage.
You might ckeck out "Wolfgang Engineering" and/or "Wolfgang Spindle". There are a number of references on Google and many Youtube videos. I have one of these spindles on a small demo machine that my son built and it is reported to have extremely low runout and runs at an advertised 20,000 RPM. Its primary limitation is that it only accepts .125 shank bits.
It is also attractively priced at around $200 for the basic spindle.