Here is the schematic as promised. I have been running this replacement car battery for several months now and I am pleased with the results. As with everything there are pros and cons. The pros is this battery should last me a VERY long time and give good cold cranking power (I will experiment more with this.). Another pro is if my car battery ends up dead for some reason I can flip a "emergency jump" switch to run a fresh spare battery with the capacitors in parallel for a quick start (I don't use a resistor here as it's a emergency "quick" feature and should hopefully never/rarely need to be used. The cons is there is not a lot of power stored in the capacitors. If your car engine has issues and requires long cranking times this will not work well. It is also not good for running the car off the battery without the engine going (example: the habit of some people to put the car on with AC fan going off the battery while getting distracted sending out phone texts before starting the car). Generally it's a good battery if your the kind of person that just starts your car after getting inside without running lots of stuff off the battery without the engine going.
For low voltage disconnect I used: http://www.ebay.com/itm/Low-Voltage-Disconnect-Module-LVD-12V-30Amp-Based-on-MCU-and-MOSFET-/371833832138?hash=item56930602ca
It is rated for 2.2 ma Load switch off and 10 ma load switch on. However I removed the 3 wire red-green led and soldered in in's place a 10k resistor (in the two holes nearest the IC leaving the third hole empty). If I recall this reduced load switch on to less than 3 ma and load switch off to less than 1 ma.
The Ballance board I used is here: http://www.ebay.com/itm/1PC-T11-350F-2-7V-2-Ultracapacitor-Supecapacitor-Balance-Board-/132051706367?hash=item1ebee521ff
It fit really well inside a battery box. I soldered thick copper ground rod on top between the posts to carry the heavy current (the board can't carry that much current on it's own (will smoke it). Underneath I used hot glue to bind all the capacitors together and to the protection board so they would support each other against movement and there would be less vibration stress against the solder joints.
The solar panel I used can be found on ebay here: http://www.ebay.com/itm/18V-7-5W-Portable-Solar-Panel-Power-Battery-Charger-For-Auto-Car-Motorbike-GIFT-/191869755141?hash=item2cac541f05
I did not explain very well I just ran the wires behind (not through) the back seats right into the trunk.
I also had to buy a good quality soldering Iron https://www.amazon.com/gp/product/B000VM3PTU/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1 as my 30 watt radio shack iron did NOT cut the mustard AT ALL trying to solder to the posts of those capacitors. ;D
Note: The diode included on the schematic coming off the positive of the solar panel is included in the solar panel I bought. If your solar panel does not have a reverse voltage blocking diode then you will need to add one there where it is shown.
The original video can be found here: https://www.youtube.com/watch?v=X8D7sNKNu-8&t=1s