In some professional service firms, this situation is called "starting working at-risk". Depending on the deal size, this often requires obtaining approval up the chain so that somebody can evaluate and ideally limit the risk involved.
I completely agree with this sentiment; sometimes starting work at-risk is a sign of good faith and goes a long way to establishing trust. Just make sure that there is a follow-up plan along the lines of "I'm working at-risk for X days. If the contract isn't signed by then, or if I've reached the first small milestone/chapter/deliverable, I stop work."
Except, in this case, it seems the OP actually had a signed contract (half way through his timeline) but Apress still refused to cough up the payment that they obligated themselves to pay. That just sucks.