OP here, I'm guessing the documentation is more advanced than the code and none of the "other ways of invoking embedded scripts" have actually been implemented yet (or bugs exist).

Commenting line 1185 in APPerl.pm lets the build happen but does not enable default_script:

$sentinelpos != -1 or die "Failed to find APPERL_DEFAULT_SCRIPT, is th
+is an old APPerl binary?";
[download]

From the docs:

APPERL_SCRIPTNAME - When the environment variable APPERL_SCRIPTNAME is set, APPerl attempts to load the basename of APPERL_SCRIPTNAME without file extension from /zip/bin or opens the perl interpreter like normal if it is perl.

export APPERL_SCRIPTNAME=hello
echo $APPERL_SCRIPTNAME
hello

DOES NOT WORK!

From the docs:

APPERL_DEFAULT_SCRIPT - If argv[0] doesn't yield a valid target either, if the APPERL_DEFAULT_SCRIPT field inside of the binary is set, APPerl will attempt to load that. This way is meant for APPerl application authors to protect against accidental rename messing up argv[0] script execution. "BUILDING AN APPLICATION FROM EXISTING APPERL" shows how to set it with "default_script", but you could also set/change it, by searching for APPERL_DEFAULT_SCRIPT in a hex editor and modifying it.

APPERL_DEFAULT_SCRIPT is not found in the binary when using a hex editor!

perl.com --assimilate does not help

Looking at perl.com with a hex editor does reveal a change when setting default_script in apperl-project.json.

Start of perl.com without default_script (minus weird chars):

MZqFpD='
ø@JT' <<'@'

Start of perl.com with default_script:

MZqFpD='
ø/zip/bin/helloJT' <<'@'