You can solve the run-detectors issue with:

    sudo wget -O /usr/bin/ape https://cosmo.zip/pub/cosmos/bin/ape-$(uname -m).elf
    sudo sh -c "echo ':APE:M::MZqFpD::/usr/bin/ape:' >/proc/sys/fs/binfmt_misc/register"
    sudo sh -c "echo ':APE-jart:M::jartsr::/usr/bin/ape:' >/proc/sys/fs/binfmt_misc/register"

You can solve the zsh permission denied issue by either (1) upgrade to zsh 5.9+ (I upstreamed a fix for this bug in zsh two years ago) or (2) use the sh -c workaround you discovered. If that one doesn't work, then it likely needs to be chmod +x. If the execute bit is set, and your sh still isn't working, then please let me know, because I'm not aware of any sh that still doesn't support APE.

See the Gotchas section of the README https://github.com/mozilla-Ocho/llamafile#gotchas