DC Water Heating Element Equivalency/Rating? ac vs dc

I've just purchased a DC water heating element from Missouri Wind & Sun... my water heater is 100 gallons, and it currently is on the grid with 2 heating elements, 220v. I think each element is something like 4500w, although I'm told they are wired so that either the top or the bottom element is on, not both at the same time. 

I started an experiment with my family of 4 about a year ago, and started instructing them to turn off the water heater at the breaker panel most of the day... when we get home from work/school in the afternoon, I then tell them to turn the water heater back on for a hour or so, then turn it off again just prior to washing up. This allows the heater to heat water in it, but as its off when they take hot water out, the cold water comes in the bottom and stays cold as you use up the hot water on top... sort of a batch heating idea, which is fine as long as you don't use the entire batch up at once.  This has led to some aggravation as they are kids and don't exactly follow the letter of what you tell them.... but I've seen a noticeable dent in my power bill.  I'm posting this in the battery/off grid section but it could go anywhere, really, I just did this as my first step in moving off grid (reducing use... next phase was a small stand alone battery bank/PV; now I'm on to a 2nd, larger stand alone PV and battery bank). Although the difference in cost was negligible in energy use, at the time my power bill was more than $230 per month so doing this made a difference.  Gas prices have come down since, but so has my usage and its now more manageable at under $100 per month.

Anyway, I just got this DC heating element, rated by them at 600w and they say its a 24v heater, but in their ad it states you can run any voltage, really, as long as you don't exceed the wattage rating. So I've purchased 2 panels to run this heating element all day, they are Trina 280w panels and they normally put out a little over 250w in the bright sun at roughly 8A. So I'll have the heating element directly wired to 2 panels at around 35v at 16A, or roughly 550w max, for maybe 3.5 hours to 4 hours per day (Hawaii).  Now, that translates to about 2 kwh per day of dc current into the water heater.  Does anyone here think that will be enough to make 100g of hot water? I would guess the water comes in at around 75F and has to be heated to around 130F, so that's 60F of movement needed.  I think with AC systems you need around 2.5w to move 1 gallon of water 1 degree F, but I don't know if that is also true of DC systems... or should it matter? If this rule holds true and I have my 4500w heater on for an hour, that means 4.5kwh per day... but this new system will only make around 550w x 3.5 hours = 1925wh = 1.9kwh per day, less than half what I'm used to before when the heater was on the grid. But I don't know if a/c and d/c watts are interchangeable.

If this math is correct, I think I have to buy 2 more panels (4 total) and another heating element and install both of them into my water heater to get about the same amount of hot water (granted, 100gal is a lot, we never run out; so I'm thinking we don't need to calculate the calories for 100gal, probably half that would be closer to real world use).

thoughts?