I use barrel aquaponics mate. Now, what are you trying to ask amidst all those figures hehe.
the displacement of water in gravel is approximately 50%. The displacement in porous gravel is approx 40%.
4 x barrel halves will use about 60 gallons in a flood cycle. So your tank is endangered by the system.
The auto siphons can be adjusted to run at differing times but thing is they continually change as root mass and bio-film is created in both the beds and plumbing.
Do you want to risk it, the timing of auto siphons does not remain constant.
For you Id recommend the options
Continuous flow, or
Only 2 grow beds or
Get a 100 plus gallon tank.
Can't help you on the solar stuff sorry, if you get good at it, you can teach me some tricks.