Dan,

It isn't unreasonable in the current climate of our industry to be a bit cautious of a new client.  Particularly one that is flooding you with an amount of work that could hurt a great deal if there were problems getting paid.

Consider approaching them with your concerns in a professional manner. 
Might they be willing to offer an initial retainer equivalent to the approximate volume they are offering you for the first month?   Once you have established a relationship, you would be more comfortable with invoicing them.

They may not agree, but how they respond will give you insight as to how professionally they handle their abstractors.

Just a thought. 

Debbie Thibodeaux
TENSTAR Corporation