To recover a portion of the cost of publishing the register of Ohio, the director of the legislative service commission may seek reimbursement from an agency of actual costs the director incurs in publishing the agency’s documents in the register. The amount sought for reimbursement is to be an amount proportional to the internet space allocated to the agency for publishing the agency’s documents in the register, and is to be reduced by the value of assistance the agency has provided to the director with respect to publication of the register. The director shall deposit reimbursements into the state treasury to the credit of the register of Ohio fund.