Yours is a matter that would probably be more appropriate for small claims court. The DLSE is typically concerned with violations of employers--not breaches of contract between private contractors.
I do apologize that I can't provide you with a more concrete answer. As you'll find quickly in the law, things are, unfortunately, rarely concrete! Often times the issue boils down to a "question of fact," which a jury must decide--not a judge or attorney.
For some further reading as to what constitutes a breach of contract and a valid excuse for non-performance on a contract, I suggest visiting this link: http://www.jamespublishing.com/articles_forms/CivilLitigation/elements_breach_contract_failure_preform.htm
In regard to conditioning the cashing of a check on full discharge of an amount owed,California Commercial Code § 3311 states that a debtor can claim a debt has been discharged by the creditor if the debtor can prove that there was an honest dispute as to the amount owed, and that he, in good faith, tendered a check indicating that is was a full and final payment in full satisfaction of the debt, and that the creditor accepted the check. Once he or she proves these elements, the debt is discharged and the creditor is thereafter barred from attempting a recovery of the remaining sums still due.
Section 3311 notes two exception to the rule. First, if the creditor is an organization and proves that within a reasonable time before the tender by the debtor, it sent a notice to the debtor that any and all instruments or communications concerning the debt are to be sent to a designated person or office, and the instrument or accompanying communication was not received by that designated person or place, the debt will not be discharged. Secondly, if the creditor proves that within 90 days after payment of the instrument, the claimant tendered repayment of the amount of the instrument to the debtor, the debt will not be discharged.
Note that it is presently unclear under California law whether the party cashing the check can cancel the effect of the "payment in full" language by crossing it out.
I hope that this helps, and again, please kindly press "Accept" so that I get compensated for my time. Thanks a lot.