For anyone who wants to try this, zstd -T0 uses all your threads to compress, and
https://github.com/facebook/zstd has a lot more description. Brotli,
https://github.com/google/brotli, is another modern format with some good features for high compression levels, which also has Content-Encoding support in web browsers. You might also want to play with compression levels (-1 to -11 or more, zstd's --fast=n); they may not map 1:1 to gzip's.
One reason these modern compressors do better is not any particular mistake made defining DEFLATE in the 90s, but that new algos use a few MB of recently seen data as context instead of 32KB, and do other things that would have been impractical in the 90s but are reasonable with modern hardware. The new algorithms also contain lots of smart ideas and have fine-tuned implementations, but that core difference seems important to note.