Surface acoustic waves (SAWs) were used to study the spin transition of the fractional quantum Hall effect at a filling factor of 2∕3. Although very distinct and hysteretic anomalies were observed at the transition in the transport measurements, no indication was visible in the SAW data. This holds true not only for the small current regime but also for the large current regime where dynamic nuclear-spin polarization enhances the effect. We suggest that this result can be accounted for by highly conducting domain walls with thicknesses of at most 1% of the typical domain size.