CalHunter, IMO you have the best suggestion. Can't just oust the cat. The relationship is strained as it is. My preference would be to take it to a shelter (well, that isn't my first preference, but I will not say what I probably shouldn't say out loud).
But as for washing the clothes... like wash them 100 times? Somebody suggested washing them with a cup of vinegar first. I don't know why that was suggested.