How about an LTspice simulation of one of the answers ?
Is this a question directed to me ?
There are two questions A) and B) in the original post with my answers in bold No and Yes.
A) Is it possible for V2 to be a constant 30V?
NoB) Is it possible for V2 to peak to 30V multiple times while V2 never drops below 5V ?
YesSo do you not agree with one of my answers ? Or with both ?
If you say Yes to question A) the it will be you that will need to prove that as I can just use an empty box or a wire between the two points and made my case.
If you say No to second question I can describe to you how it will work but the diagram I offered as an example should be sufficient.
The capacitor will be disconnected from the two box terminals and connected to the output of a DC-DC boost converter.
The boost converter can be a max power point so one that maintain a constant voltage at the input and takes what is available.
So say DC-DC MPPT is set to 5V then the other 5V will drop across the 100Ohm resistor meaning 50mA will flow trough the circuit.
5V * 50mA = 0.25W are available with say a 70% efficient DC-DC converter 0.175W are available to charge a large electrolytic capacitor connected at the output of this DC-DC converter.
When this capacitor gets to 20V some analog trip circuit can disconnect the DC-DC and connect the capacitor between the two connection points on the green box.
Thus for a short moment V2 = 10V + 20V = 30V
It can get way more complicated than this with a microcontroller and current measurement to calculate exactly what the resistance value is and what the battery voltage is but this are unnecessary complications just to say that it can be done.