For the first payment, I signed a contract as soon as they asked me to, and they still didn't pay me for months.
For the book, my refusal to sign almost certainly delayed payment. I modified the deadlines, removed clauses about ongoing work (dealing with errata etc.) that I wasn't going to do, etc., but nothing major. They refused to accept it, but immediately changed their tune once I pointed out that they couldn't actually publish what I wrote without a contract, and there was no way I was signing without those changes.
Did you attempt to modify the deadline to a future date, and if so did they refuse to accept that version of the contract?