When the agreement calls for payment of the utilities by the landlord, but fails to specify a time for the payment, the law implies that the payment should be made within a reasonable time. 22 months is more than a reasonable time for the landlord to begin reimbursing you.
The landlord does has a right to sue you for unpaid rent, unless the lease states that you can use your security deposit for your last month's rent.
Your idea of sending a letter stating that if no response is received, you will assume landlord's agreement is a good one, even though it is not legally binding on the landlord.
Under Civil Code 1950.5, security deposits can only be used to pay unpaid rent, repair damage beyond normal wear and tear, clean the premises and remedy future rent defaults, so that any remaining balance must be refunded.
The landlord must provide the tenant with entitled to an itemized statement of the deductions from the security deposit within 21 days. Civil Code 1950.5(g). If the landlord fails to do so, the landlord must refund the full deposit, but can sue for damages. Granberry v. Islay Investments, 9 Cal.4th 738, 745 (1995).
If the landlord fails to refund your security deposit, you should consider making a claim for bad faith retention of your security deposit, which allows for an award of treble damages. Civil Code 1950.5(l).
Ultimately, you may have to sue the landlord in small claims court for the reimbursement of the utility bills.
Generally, it is tough for an attorney to provide any recommendations on a contract that they have not reviewed. With that being said, damages sustained by breach or nonperformance under a contract are recoverable in small claims court. Attempting to resolve these matters with your landlord is highly recommended based upon the need to name previous landlord's as references when you move into any new apartment. If there is no avail in resolving these matters, small claims court is probably the best way of adjudicating this dispute.
This response is not intended, nor should it be construed as legal advice. Any information provided is for educational purposes only. The exchange of communications through Avvo.com and similar social media does not establish an attorney-client relationship with me or my office. To schedule an appointment for an attorney-client privileged consultation, contact me at 909-860-0342. Thank you.