The more advanced your predictor is, the slower your compressor gets. OP has 600 Million moves to encode, how long does it take to ask Stockfish for its opinion on 600M board states? (and then again, every time you want to decompress) (not a rhetorical question btw, I know little about chess engines)

I suspect the sweet spot here would be to use a much worse chess engine for the predictions, giving faster compression/decompression at the expense of the compression ratio.