WLED Randomly Turning On

Precisely.

The foil on the strip is not at all substantial and several Amps current draw will result in significant voltage drop

If nothing else, because the blue LEDs have a higher threshold voltage, when set to full white, the colour will tend to yellow or even orange at a distance from the power injection. This does not of course explain the whole strip going to a uniform colour, but is a limitation of longer lengths of LED strip.

Keep all wiring bundled together - power, ground and control signal. The power "bus" that runs alongside to feed the strip at regular points should preferably not be separate.