RGB LED Matrix spread over 400 square feet (43 square meters)

This project isn't really that bad. I'd use an Arduino Mega (for the larger SRAM, mostly) and see what can be done with WS2811 pixels. Break up the array into several 50-100 pixel chains. It would still be a lot of soldering, unless you got some small custom boards and cables made. I don't see any easy solution coming in much less than $1500...that's how projects work, you have to trade knowledge and work for money in one direction or the other.