1. Of course, the larger the capacity, the longer the duration is. But you come across with the physical size of the cap. I would pick DB-5R5D105 from your list.
2. Have a serial diode to your PIC power line and put the cap after diode. You may have an input pin to detect the power loss before the diode, and start your power saving mode immediately WHILE the cap is still powering your PIC.
This is my idea in theory.
"If the Earth were a single state, Istanbul would be its capital." Napoleon Bonaparte
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