Since it's a serial control line couldn't one make seven independent strings to speed up the refresh rate and drive it off an 8-bit bus?
/me thinking it would be a good tetris platform...
Not sure about the original LED used there, but with the popular LED tapes built on the WS2812, you should be able to drive at least 200 of them within 20 milliseconds.
That gives you the idea, then yes if you want to run more LEDs then use more outputs and drive them in parallel.