My advice regarding good quality inverters - Goodwe ES, Sunsynk (which is one of the top 3 inverters in the US under the brand name Solark and Victron Multiplus ii.
These are bidirectional, brilliant functionality and all have COCT approval which theoretically means they should be approved all...
The new Lithium Ion Phosphate LIFEPO4 generation of batteries work.
Their charging cycles are controlled by the built in BMS(BATTERY MANAGEMENT SYSTEM)
Prices aren't too bad as well.
Definitely worth going for this option.
12V 4kw is over 300A DC!