Connecting solar panel and batteries of different voltages in series
It might sort-of work under the right circumstances, but I'm betting you don't have them.

Inverters typically take large currents at the input voltage in order to produce useful power at the higher one.  This means that, for your scheme to work, the solar panel must always provide enough current to supply the inverter, ie. be in good sunshine and be capable of suppying the full current required by the inverter while maintaining 16V+.

That's going to be a big panel, and you may have to stop the planet from rotating:)

I don't think your scheme will be successful.