FWIW, You can get DC water heater elements and skip the cost/inefficiency of the inverter.
https://smile.amazon.com/Dernord-Immersion-Submersible-Element-Stainless/dp/B017VT68XA
Those elements are in parallel for 300W. So it about 150W/12V=12.5A each. (12V/12.5A~=1ohm.) Running just one might still be a lot for your small controller & battery. You can put both windings in series for ~2ohms. That makes it a 12V/2ohms=6A load = 75W (which is 1/4 the orig 300W.)
There may be a potential issue with the DC elements they look good on paper. At 300 watts it would take 150% more time to heat the water to temperature in a 50-gallon water heater. The typical water heater has 2 elements at 1500 watts each using 220VAC.
When I worked as the energy manager at a college, we installed solar water heating systems. There are many types, more efficient and models now than there were 15 years ago.
A friend has a 15x25 foot swimming pool. He was going to install a solar electric system to run the bumps and pool heater. He was going to have it done by a local solar system. In the summer months he pays over 600 bucks a month. In the winter his bill drops to 200-250 bucks a month when not using the pool heating system.
The contractor was going to charge 20K to install an electric solar system to run his pool. Well, he did not have 20K to spend on a pool. I asked him if I could look into using a HW solar system as a DIY project? So, based on pool size and keeping the water temp at 80 degrees the HW solar parts and equipment was 4k. Based on OAT of >70 degrees F, it would take about 5 days of sun to heat the water to 80 degrees. Once it reached temperature it would stay there with just minimal use of the solar.
So even in the winter with an insulated pool cover the pool he can swim in the winter and the pool stays at 80 degrees. With just the 120vac pump running it uses 1200 watts of power. His electric bill through the year now is no higher than 250 bucks. So, in 14 months the solar heating system has paid for itself in savings.
The only difference in a HW solar for a home is the number of solar elements needed to maintain 125 degrees. If you have an oil furnace/wood stove, you can use the wasted heat from the stack to heat the water too which is really cheap to install. Solar HW heating system is less expensive to install. You can also put a HW coil in your AC/Heat pump system and heat your home.
Just food for thought.