But that might get shortened to "Don't start work". Contracts are notoriously difficult to finalize. If you don't take the risk, someone else probably will. Best is to establish trust with counterparty.
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.
You are correct. Contract signed in September, which Apress was instantly in breach of since they didn't even bother to change it to suit the lateness, and payment for that one didn't happen until late November.