Matthew,
TAS/8 + 3 gives better results from 0kt up to 330kt which covers the usable speed range : 60kt, 12.4° (ultra lights) - 220kt, 31.1°.
However, dividing by 8 is harder than dividing by 10.
TAS/8 + 3 actually gives an error below 3.1% in the range 90kt - 300 kt.