I do agree with you, and the difference is that it was a unilateral decision on his part, to leave. The two of you didn't agree on how to split things up, or who would live where. Neither temporarily nor in the longer term.
He also can't just tell you that you are getting the house and he's keeping whatever else. If he is serious about that, you can have him file a quit-claim deed at the court house, giving up all rights to the house. If he's not on the deed, then a letter stating he has no interest or rights to the equity in the house might suffice. If he won't go for that, then you need to tell him that if he DOES still have rights to the house, then he still has responsibilities, as well.
You say you have to do these things because he won't and it "has to get done." But it doesn't. Yes there are consequences, and if you are the one with your name on the mortgage, and the good credit rating, then you have more to lose than he does. Which is why he can take advantage of that fact. He'll let you do all the work, sit back, and collect half the equity when you sell.
You are looking for a job back home, right? This is why I think you need to talk to a realtor. Not that you can't sell it yourself, but that you may not be there or have the time. Bigger realty offices have specialists in property management as well. They could market the house, but also rent it out for you in the meanwhile if it didn't sell. Manage the lawn care, maintenance, etc., while you are starting over back home.
You leave it all in their hands, and they take their fee out of the proceeds of the sale. If you get all the proceeds, you are no worse off and have a lot less headaches. If he gets half, then his half of those expenses is already taken out of his half of the proceeds.
