While your home might have negative equity it is still a bargaining tool that will give you leverage.
I am stunned your attny would suggest you sign it over and then say support may be requested at a later date. You don't GIVE UP something until you GET something.
You don't hand over your biggest asset (and even with negative equity it is still an asset) in the hopes you might get something in return if you ask.
If your H and his attny are not responding to the documents you and your attny are sending as per the time frame established by state law then use legal procedures to get them to respond.
The judge isn't going to by "fair". They are going to go by state law and I am going to guess you don't live in a fault based state.
I would urge you to educate yourself on state law.
My C always says the true nature of what people really are comes out in a divorce.
