It's confirmed: we need to move. Our landlord is going to have to make major structural changes to the addition of the place we're currently renting. He gave us the option to be let out of our contract without penalty, and since we're not sure that the fixes he has planned will completely eliminate the smell (and the asthma attacks), we decided to accept the offer.
We've been able to find another place. It's smaller and a little farther away from work, but we made darn certain this time that it wouldn't have any potential mold problems! It's a little less in rent, as well, so we'll be better financially, too.
I'll go into more detail of the situation a little later.