Simple solar panel + supercap powered arduino
The HT7325 has 500mW of maximum power consumption. If your solar panel is really able to achieve 1.5W output most of it will be lost as heat in the HT7325 and it will be too weak. 

I think there are LDOs with reliable overcurrent and overheating protection which could be safely operated in this rare condition.

I think you could leave out the second 1.8V LDO if you don’t need a specific, stable voltage (for example for interfacing with other chips (powered from a different source) or ADC/DAC). The ATmega328 has an operating voltage from 1.8 to 5.5V.