Stanching rhymes with:
branching, ranching, branching, bunching, clinching, crunching, drenching, entrenching, flinching, inching, launching, lunching, lynching, munching, pinching, punching, quenching, ranching, retrenching, unflinching, wrenching
Stanching sounds like:
sodomizing, stinginess, stinging, stinking, stoneking