Under procedures adopted by and subject to the approval of the Department, an audited partnership or a tiered partner may enter into an agreement with the Department to use an alternative reporting and payment method. However, the Department shall enter into such agreement only if such audited partnership or tiered partner demonstrates, to the satisfaction of the Department, that the alternative method is reasonably expected to provide for the reporting and payment of taxes, penalties, and interest due under the provisions of this article. Application for approval of an alternative reporting and payment method shall be made by the audited partnership or tiered partner within the applicable time period specified in § 58.1-399.1 or 58.1-399.2.