I wonder how a big chunk of those 4A DC you will lose with inverter and wall wart. 1-1.5A total losses of the wart and inverter. Mostly in the wart.
Unless you are on a mid-small solar, living fulltime with no generator - which I think you are not - you will hardly notice daily 10 AH loss, or whatever long you have to run that appliance.
But, if you really need to save energy, get one of Meanwell DC supply units. 5-6% loss VS 30-40% of your regular AC-DC wart. Cleaner DC too. Cheap warts often output poorly filtered voltage.