I have not exactly looked into the values. The background of my concerns is, that electrolytes have noticable leakage: There is internal current discharging them, similar to cheap rechargable batteries.
When you charge a high capacity cap via 2MOhms @ 2V= 1uA, this could just be enough to uphold its charge level, if ever 
Edit:
I looked it up now. Your goldcap (5.5V 0.1F) might work, its leakage is < 30uA; charging through a 100k @ 4 volts will give 40uA.
However the full charge time will have nothing to do with your expectations,und will heavily depend on environment temperature....
O.k. 1k can provide 4mA, which is definiitely fine. 1k*0.1F = 100 s = around 1.5 minutes.
A .1F goldcap will be around 3 USD.
Maybe 10k and a .1F goldcap will be compromise...