WS2812B LED Strip Not Drawing Full Amperage
Check the voltage on the far end. Your LEDs sound like they're not being supplied with sufficient voltage, and it may be that the current you're supplying right now causes a sufficient drop by the end of the string. 4.5A is a lot of current for a system like that to handle and it's likely there's a significant voltage drop along the LED strip. 

It appears the strip may not be designed to supply current along its whole length while every light is at maximum brightness.

I'd start by supplying the 5V and GND to the center of the strip so there's half the current on the board running in either direction and so the strip runs half the length from where you connect it to the end. Then measure the voltage at the end and if you need you can add secondary connections to deliver 5V to the portions of the strip that are falling below the 3.5V VDD minimum specified for the LEDs, you can make more connections to VDD and to GND to bring that region of the strip back to a 5V supply voltage.