Precipitated DNA cannot be fully dissolved

That step is not meant to fully dissolve the DNA. As the protocol says, "Add 750 μL of wash Buffer to the DNA pellet and gently resuspend by pipetting until fully dispersed. Transfer the entire suspension to a miniprep spin column..." So the goal here is not complete dissolution, but just getting the pellet dispersed well enough to transfer. Since the buffer is still ethanol-rich, the DNA is not expected to fully dissolve at this step. The pellet just needs to be dispersed well enough for transfer onto the column. In our hands, the pellet does not need to be broken up very finely at this step. As long as the suspension can be transferred onto the column, we do not observe any difference in the final result. If transfer is difficult, the troubleshooting section says, "Fully disperse in 750 µL of wash buffer before loading; trim the pipette tip to ease transfer."