I am curious of what state you are. I had no money, was not served with any papers, was just gathering info and got three appointments of my choice because I could get even more. By the way I am in Colorado.
My house was not in my name either and is still not in my name until I can refinance it in a year after my D decree. But it is mine, I got the house because 50% was mine.
In your case, just like V said, if your H bought the house before you were together, and I don't mean married, maybe you were together before being married. You are entitle of some part of the increased market value. What is the price of your house now, minus the price of the purchase years ago.
Your poor H may have 401ks, pension. It is all yours too. Look at this as business.
And I agree with V and Squiggy, stop trying and do it. When you talk to a L, don't say that your H just left but he is such amazing man, giving you money, support, house. First, he is not giving you anything that is not already yours. Second, the L won't waste his time in a foolish couples fight. To get what you want from the L, and this is what you need right now, you need to say that your H is a bastard and you are looking into filling yourself because he is the worst man in the world.
The L will have appointments tomorrow, child care and snacks, they will tell you all what you need to know and if you have some numbers, financial info, they will try to calculate stuff around your situation.
Payment can be done with a credit card. Once you have some picture of what kind of money you may get from the D and you may be able to pay the L with the money that comes from the division of assets. I did this. I did not have any money either.
**** About the T-shirt, I also think you are going LOCO, get that shirt and put in a box.