Okay, I am going to try to assist you with this question. I am going to try to be very honest on what I see going on here. First, he has said that he does not want to be in a relationship with you, nor does he want to reconcile, nor does he want to go to counseling. It sounds like he really does want out of the relationship. It may not be because of you, it may be like you said, because of his busy lifestyle.
But one thing is for sure, he does not want to be in relationship with you right now. The only way that you can reconcile is if he wants to try to work on things with you. He does not even want to go to counseling. So it is going to be hard to get back into a relationship.
As far as you looking for an apartment for him and him not moving out. I think your assumption is correct. He more than likely wants to have his cake and eat it to. You guys were together for six years. I am sure that he still cares for you, and wants some benefits of a relationship without actually being in a relationship.
For men, some want the experience of a girlfriend. But still want the freedom to do what they want, and it will be okay, because you two are not really together. With that being said. Do not let him do this to you, and give you mixed messages. I think it may be best that if he does not want to be with you. Have him move out of your apartment, so you can move on with someone who does want to be with you.