After a failed attempt at building my own custom cables to link LEDs together and to the Raspberry Pi, I ended up taking the easy route and using wire wrapping. turns out the connections are strong, wires are light, and provided that the i2c clock is slowed down enough (baud rate is not exactly important for this application) it's pretty stable.
On the "brains" side, I've decided to go with a Raspberry Pi Zero W because it's small and lightweight, and wifi is built-in.
On the software side of things, I elected to go with Node.js as the platform because i'm fairly proficient with it, and wrote a couple of modules to run as daemons on the Pi: a "monitor" module that reports on my personal IoT solution (based on Azure IoT Hub, I like to know when and how my devices are running) and a "ledtac" module that gets the weather, and converts the Metar information and drives the LEDs. All of this is orchestrated using PM2 and the OS is a hardened, auto-updating version of Raspian Lite (Stretch)
What remains is to build a custom frame, and check if everything runs smoothely over the course of a few days. the goal of this thing being to run all the time, I want it to be stable and not a project that runs a few minutes and disappears in a drawer...