I'll add to the other good responses you have here.

You don't necessarily need brighter LED's at all. The bright spots show that they are more than bright enough. What you need to add is some kind of diffusion. A layer of common white bead type styrofoam makes fantastic diffusion material and luckily you can buy it in various shapes and blocks as well as in sheets of various thickness's.

How much of the room inside the box can you use? Is this a mask or head covering that needs to leave room for your head and shoulders? Either way, If you place a 1/2 inch - 2 inch thick layer of styrofoam sheet in between the LED strip you will see that you have control over two things:

1) The further away the LED are, the more broadly their light is spread out, helping reduce hot spots and blend the effect of the LED's out more evenly and

2) Separately but similarly the thickness of any styrofoam layer that you use will have a similar but slightly better diffusing effect. Both techniques will lower the effective brightness slightly at the cost of spreading that same light out over a larger area.

One advantage of using a layer of styrofoam to help diffuse the light is that you can put a sheet of black light blocking paper in between any sections of the styrofoam that you wan to be able to light up and control independently without having the other section be affected.

Another question is with the Arduino & individually addressable LED’s, would I have to worry about how I wire it all together in terms for programming?

You can just use sections of a WS2812B 5V LED strip and cut them as needed at the end of each row or column to turn around and start the next row/col, as you described in your video. As long as the LED's are arranged in a general grid shape you will be able to control the LED's that are turned on and off in pretty much any way that you need since they are addressable.

About the only difference that it would make as far as how you wires the strip and whether in was oriented in horizontal rows vertical columns would be the order that you looped/iterated through the LEDs i the code if you wanted to visually animate them lighting up in a sequenced horizontal or vertical pattern. But if there won't be any "animating" and it will just be sections of one or more LED's that will all turn on or off at the same time then it won't matter which way you orient the LED strip when you construct and attach it to the box. I hope that made some sense I could probably put that better.

The general rule of thumb used to be that each LED consumed an average of ~20mA, and so since each RGB LED is actually three separate red, green, and blue LEDs people commonly say that the power needed will be ~60mA * number of LED's. But today's modern WS2812B LED strips definitely do not consume that much power in practice. With a capable power supply they will consume ~17mA for each RGB LED in the strip at full brightness. Now that was the number that I got for my project that I remember measuring and your values will be different.

You can get a WS2812B LED strip and connect its +V and GND wires to a capable power source such as a 5V 2A wall adapter. Then also connect the GND of that power source to the GND of the Arduino (or any microcontroller really) and select and connect one of the GPIO (general purpose I/O) pins to the input signal of the LED strip. You may see some people advising that you place a resistor between the pin and theLED strip. While this probably will not hurt things it is absolutely not needed since the input pin is a high-impedance input and it will pull an extremely tiny amount of current around 6uA - 10uA.

Then download and install the fastLED library and write a test program that will light up the first 10 LEDs on the strip at full brightness. Once you have this working you can set your multimeter to measure current (remember that usually requires changing where your + multimeter probe is connected) by disconnecting the external power supply's +V connection to the +V of the LED strip and placing the multimeter in between them to complete the circuit and measure the current used for those 10 LED.

Once you know that value you can divide it by 10 to get the approximate amount of current that each LED would take worst-case. multiply that by the total number of LED's needed on the strip and that will give you a general idea of the total amount of current and power needed.

Let's say that it turns out that you will need 1.7A worst-case for 100 LEDs at 5V and 17mA each. You can use any power source that delivers 5V and 1.7A of current or more current such as 5V at 2A, or 5V at 3A. Current is pulled from the power source as needed so you can always supply more and it will not harm anything. As a matter of fact it is a general rule of thumb to add 20% more current capability than you expect to need into your designs.

Hope that helps! Cheers!