Your accounting of the goings on and your statements as to the issues involved sound reasonable and quite well put.  If you have paid trough the end of the month and the landlord does not intend to pro rate the rent as originally agreed then you are entitled to as much access as you wish.  Second, most states only require that an apartment be "broom clean" when they leave.  You need not scrub anything white, as they say, unless say you got it unusually dirty.  Tell you landlord that you do not want workers in the house until you have completely vacated the apartment and you have yet to do so.  additionally, make sure that you do a walk through with them prior to turning over the keys and have them sign something that says that everything was ok.  If they refuse to comply take them to court.  Good luck.