4 years isn't going to help. A couple of months is reasonable. STBX is exactly right about the lawnmowing thing. And, that is exactly why him storing your stuff at your residence is a problem. STBX should have no household duties. Nor should he have any household benefits. This is a *divorce*. Your lives will be separate in the future. He doesn't get to keep the small bit of his old life because he finds it convenient.
Talk at the mediators, you don't need to talk before then. You don't need to justify or explain it. All you need to say is: "I will consider allowing you to store your stuff at my house for a maximum of 3 months if you sign something that says I am not responsible for any damage or loss to it."
As for the house and him owning, I urge you to do whatever you can to make that NOT the case. Take out a loan, borrow the money from family, max out the credit cards, but pay him off now. It is soooooo not worth having that tie to him for five years. It would have to be an unmanageably huge chunk of change for the financial costs not to be worth your increased quality of life.
And, he'd probably be willing to take a reduced amount (maybe 80 or 90%) of the total to get the cash up front.
A word of advice: quit looking to STBX to perform any husbandly duties or to do things for you as a friend. He is not your friend. He is your husband only legally. In every other way he has left the M. In any way that matters in a non-technical way, he is no longer your husband. He is not someone you should look to as someone who plays a part in how your future life goes in anyway, other than related to support payments and how to exchange the kids.
