Electronic – Low power device with high current peak

I'm creating power supply for controller that usually operates with very low power consumption, but sometimes needs high power. To make the situation harder there is "sometimes" external power present (mostly not). So the whole circuit must live from super capacitor.

The problem I have is that I do not know how to replace the 7 ohm resistor on left side with some 'intelligent' circuitry that will primary power the controller and use ONLY remaining power to charge super cap.

Controller works in two modes (using 2 to 5 V as input voltage):

1. low consumption mode taking 1 uA to 20 mA (peaks of max
   30 ms and minimum 5 s apart, usually few hours apart).
2. High power mode consuming cca 200 to 800 mA, before entering this mode the controller switches on the main supply and checks if input voltage is more than 3.5 V, should the voltage be below the controller waits with mains on in low power mode and resumes high power operation when input is over 3.5 V

There is also push button for cold start, but normally should be not needed as in case the controller recognizes less than 2 V on input (shortly before dying) it switches the mains on, so as soon as mains will be present the operation will be resumed automatically.

Now the problem in detail: There is 7 ohm resistor that is 'necessary' as the super cap will burn the 5 V power unit on cold start. But on the other hand it prevents high power operation of controller as there is not sufficient power for the controller (big voltage drop). For this reason I need to replace the resistor with something that consumes 0 A (real 0 or less than e.g. 1 nA) in case there is no external power. In case there is external power it should primarily power controller, if there is any remaining performance of the power source it should be used to charge the super capacitor.

Any ideas how to create this kind of circuitry? Thans for any help.

Until now I was trying to use transistors to monitor voltage difference between cap and power source, but this is not sufficient (and has high power usage when no external power applied (10 uA) depleting the super cap too fast.

Block schematics below.