Inrush current for LED strip circuit
Your problem can be summarized by asking how much inrush is required to energize a reactive circuit.  Reactance can be caused by either inductance or capacitance or a combination of both.  Basically, any kind of Z will need to charge up and store energy.  

What you are describing is pure DC feeding capacitors and trying to charge them before the LEDs light.  That is basically what a ballast does for flourescent lamp.  But that is because it needs to charge enough to achieve the breakdown voltage of the gas inside.  Then it can basically feed simple power to maintain the light.  If you recall the old "starters" they were the switches that would allow it to do this.  

The best way to mitigate such a problem with LED strips is to simply use a large enough power supply that can handle the total current and do not add extra caps.  

LEDs alone do not exhibit the kind of inrush current that any kind of reactance does, whether inductive or capacitance.  LEDs present as pure resistors.  They do not need a starting voltage.  

Just feed them the power they need and the only limiting factor will be the resistance of the wiring of a string.  I.e., if you do not provide enough power then you can only light a certain length.  The strips do have conductors integral to them but they are not of a very heavy gauge so there is voltage drop just due to the length.

Instead of using capacitors to extend that length it would be better to feed along some larger wire along the string to directly power the next section.  

I have had strips that worked fine until they used blue, then the far ends would not be as bright as they were when they were green or red.  One power supply separately feeding multiple sections is the key to bright LED strips.

Bottom line is to think in terms of resistances.  Both the wire and the current requirements of the LEDs.

And keep in mind that different LED colors require different amounts of current.  That can mean that if your strings  change color, you need to adjust your power supply setup as if they are all white (R+G+B) or all blue.  Those take the most current.  If it will work for white, it will work for all the other colors just as well.