Posts#42, 43, 44, 45, 47 above.
Hy Tony,
The OP has wisely chosen a low switching frequency which minimizes any problems with self resonance etc that seem to trouble you so much.
In terms of maximum power point tracking (MPPT), that can be done by the MCU, if necessary, by monitoring the solar panel output voltage and current and adjusting the pulse width modulation mark-to-space ratio accordingly. The OP has stated that he is presently doing this manually by adjusting a potentiometer.
The graph you show for maximum power transfer and your statements have confused the OP as evidenced by his question about placing the solar panels in parallel rather than series. There are two aspects:
(1) Power transfer from the solar panel
(2) Efficiency of the switch mode power supply.
and you have not clearly differentiated between the two.
I find that type of graph confusing anyway, although it is used quite often. The characteristic of a solar cell is essentially a constant voltage (band gap) with a varying current capability proportional to the intensity of the incident light. It is not, in principle, a constant current with varying voltage. As such it is very similar to many load lines.
Because of this, in principle, MPPT is not exactly rocket science, although to read some of the information on the net you would think otherwise. No doubt MPPT gets more complex with some solar panels, and if you are trying to extract the last 5% of power.
But the OP has not asked about maximum power point tracking. He is merely asking why his inverter is inefficient (not working).
To a first order approximation a buck switch mode power supply does not care what the input voltage is, as long as it is a few volts above the output, as it operates on constant power not constant current like a linear regulator.
I had already explained about the inductor value and showed the calculations.
I know you are a learned fellow, with a great deal of experience, but in general it is important to make sure that theory, advice, and warnings are targeted at the project in hand, both in principal and degree and to answer the OP's questions in terms commensurate with his level of expertise.
spec
PS: Here is an ON Semiconductor application report which includes an overview of solar panels:
http://www.onsemi.com/pub_link/Collateral/DN06054.PDF