The Commissioner of Social Security may waive the limitations specified in subparagraphs (A) and (B) of subsection (e)(1) on an individual’s eligibility and benefit amount for a month (to the extent either such limitation is applicable by reason of such individual’s presence throughout such month in a hospital, extended care facility, nursing home, or intermediate care facility) if such waiver would promote the individual’s removal from such institution or facility. Upon waiver of such limitations, the Commissioner of Social Security shall apply, to the month preceding the month of removal, or, if the Commissioner of Social Security so determines, the two months preceding the month of removal, the benefit rate that is appropriate to such individual’s living arrangement subsequent to his removal from such institution or facility.