Longshoremen rhymes with:
chairmen, abermin, aldermen, assemblymen, benjimen, brahmin, centromin, chairmen, clergymen, comin', congressmen, congresswomen, countrymen, cremin, crewmen, domin, elamin, ermin, examine, fermin, firmin, fishermen, fremin, freshmen, frogmen, gentlemen, guardsmen, herdsmen, hermine, jasmin, jazmin, jermyn, jessamine, jessamyn, lobstermen, merchantmen, militiamen, newsmen, norsemen, petromin, policemen, pondimin, salesmen, shimmin, solemin, spokesmen, sportsmen, statesmen, superwomen, termine, tribesmen, vermin, westmin, wilhelmine, workmen, yamin, yasmin, yasmine, zemin
Longshoremen sounds like:
langerman, langhorn, langhorne, lohengrin, longhorn, lunchroom, lungren