Table C.7 in the ASQ:SE-2 User's Guide contains the cutoffs for each questionnaire interval (see ROC cutoff score column). The ASQ:SE-2 Technical Report includes a specific discussion of the ROC analyses and why means and standard deviations weren't used for ASQ:SE-2 (see pp. 193-194).
In this situation, providers need to be sensitive to parents' concerns and feelings, especially if it is likely that ASQ-3 items will be difficult for the child. Asking parents about the strengths of their child and starting there is a good idea. You could even ask parents to complete the ASQ-3 areas out of order to …