Can my former employer not pay for the full vacation balance I have upon termination?

In your state, vacation must only be paid out on termination if there was an employment contract, or *possibly* an employee handbook or manual which had no limitations on its enforceability (i.e. did not contain language to the effect of "nothing in the manual creates a contract of employment" or "polices subject to change" or "all employment is employment at will") and which stated clearly that vacation will be paid on termination of employment, since such a clear, unambiguous, and unrestricted policy statement can sometimes be held to create or establish a contract. In the absence, however, of any contractual obligation on the part of the employer to pay out vacation when employment ends, they are free to not do so--i.e. to either not pay you at all, or to pay you only so much as they may choose. Therefore, unless you have a contract, you cannot force them to pay out the rest of the vacation. Because vacation is not required, your state takes the line or stance that it only has to be paid out on termination if the employer agreed it would be.
You could likely sue (e.g. in small claims court) for the expenses. The law generally holds that if you incurred the expenses for legitimate business purposes after being told (or shown, by prior practice) that they would be reimbursed, that forms a contract (e.g. an oral or unwritten one) that you will be repaid for the expenses you incur for work. You could therefore sue based on breach of contract for the money, and also based on "unjust enrichment"--the idea that they should not be allowed to be unfairly "enriched" by having you pay expenses for them, when you reasonably expected to be reimbursed and they knew you only incurred the expenses in expectation or anticipation of reimbursement.