The meanings of modal verbs would and could are not equivalent. Would indicates willingness while could indicates ability: "I am willing to go because I like employees (would)" versus "I am able to go because employees' houses have access ramps for my wheelchair (could)." There is a politeness factor that enters into the use of modals, but politeness is a feature of modal use that is different and separate from meaning. The same is true for probability and possibility; these are features that are different and separate from meaning.
To give an illustration of these distinctions: Politeness might correspond to how you're dressed; probability/possibility might correspond to the room you are standing in; while meaning corresponds to what you mean by what you say while you are dressed as you are and standing in a given room.
When Burns says, "I would even go to an employee's house," he is indicating, firstly, with would, that he is willing to go. He is indicating, secondly, with even, that going to an employee's house represents an extreme action. The adverb even has one meaning, out of many, that is explained as "used to suggest that something mentioned as a possibility constitutes an extreme case or an unlikely instance."
When would (willingness) is put together with even (extremity), a good paraphrase of the sentence is, "I am willing to take the extreme measure of going to an employee's house." You must not try to paraphrase the modal would by substituting the modal could because, though they share some features, they have different and separate meanings.