Definitely use OctoWS2811. You'll need the non-blocking feature to be able to reliably receive DMX message which arrive while the LEDs are updating.
There's an example which plays uncompressed raw data from the SD card to 4320 LEDs. It worked great on Teensy 3.2, using about 50% of the CPU time (mostly for the SD card reading) while maintaining 30 Hz refresh and streaming mono 44.1 kHz 16 bit audio. Probably start with that code.
If you're only going to play 1 video clip at a time, so if a new message arrives while you're still playing another file, you'd immediately close it and open the other file and make the next LED refresh the 1st frame of the new file, I'd say this should be pretty do-able. You'll probably want a faster card like Sandisk Ultra to avoid latency.
If you're wanting to play 2 of more files at the same time, with some sort of masking or blending algorithm, it may or may not be do-able. The Monolith Synth LED visualization alpha blends a few dozen layers, so the blending part could probably work. We are able to play 2 WAV files together with the audio library, sometimes even 3 with better quality SD cards... but the unsophisticated Arduino SD library which reads 1 sector at a time may become a limiting factor if you try to read multiple files. Again, the SD card make a huge difference. There aren't any reliable specs. The speed class is for sequential access by cameras and camcorders. Look for a card that has good "4k random read" benchmark.