Anthony D’Amato is a very busy man these days. The front man of the uniquely quirky soul band Remember Jones, he has been on a national tour all summer. What had been planned as a well-deserved couple of days off before the tour was scheduled to end at Bird and Betty’s in Beach Haven this Saturday night had been filled instead with shows in Woodbridge, Long Branch, Woodstock, N.Y., Killington, Vt., and Atlantic City.