Long-overdue rhymes with:
overdo, overdue, overdo, overdue, perdue, purdue, urdu, adieu, ado, badu, chengdu, deux, dew, do, doo, douwe, du, due, katmandu, ledoux, outdo, overdo, overdue, pas-de-deux, perdue, purdue, redo, seydoux, subdue, undo, undue, urdu, yabbadabbadoo
Long-overdue sounds like:
langford, langsford, lankford, lansford, longobardi, lunceford, lunsford