I can tell you are a loving mother. I can tell your X is not a loving or caring father. The best thing you can do for your daughter is to contact an attorney or find one through the courts imho. Then, you can find a therapist for her.
Neglect and abuse have similar outcomes for anyone. Treating the victim is treating the signs & symptoms instead of the insult on your child. Take a tally and see who would use the laundry room as a bedroom for a human child. That is usually reserved for VIP pets. Pets don't mind the noise.
Depending on the severity of the neglect, you can request a reduction of the 60/40 custody order or parenting plan. You can reduce time to weekends unofficially. (I don't think he'll mind) Demand your daughter has a safe & quiet place to sleep in writing. Or you can let him off the hook to terminate the abusive parent’s custody or parental rights.
Think of what a trained advocate for children in the court-system would do. Your daughter may go to therapy even after you X dies if he keeps neglecting your child.
Save some money and spend it first on a consultation with a lawyer. Maybe directly ask your X what is the minimum he would like to spend with his flesh and blood.
Custody arrangements are not exact rules. They are just the safety net or a fallback line. As long as your X doesn't object anything is fair game. This option only costs you an email and your daughter's conflicted peace of mind. Keep everything in writing.