Answering my own question:
From the App Store, grab the High Sierra installer. It will launch "Install macOS High Sierra" after the download completes. Click "Continue", accept the licensing agreement, select the install drive, then the installer will prompt for an admin password. After that, it will begin downloading to "/macOS Install Data" on the local machine.
The main data file is
/macOS Install Data/InstallESDDmg.pkg
When the download is complete, the installer will prompt for a system restart. Before doing that, inspect the download directory:
sudo find /macOS\ Install\ Data -type f -exec ls -l {} \;
-rw-r--r-- 1 user staff 328 Dec 4 19:03 '/macOS Install Data/AppleDiagnostics.chunklist'
-rw-r--r-- 1 user staff 2613173 Dec 4 19:03 '/macOS Install Data/AppleDiagnostics.dmg'
-rw-r--r-- 1 user staff 1948 Dec 4 19:03 '/macOS Install Data/BaseSystem.chunklist'
-rw-r--r-- 1 user staff 478740408 Dec 4 19:04 '/macOS Install Data/BaseSystem.dmg'
-rw-r--r-- 1 user staff 2124 Jan 8 08:39 '/macOS Install Data/index.sproduct'
-rw-r--r-- 1 user staff 4706541399 Dec 4 19:09 '/macOS Install Data/InstallESDDmg.pkg'
-rw-r--r-- 2 user wheel 1584 Dec 4 19:09 '/macOS Install Data/InstallInfo.plist'
-rw-r--r-- 1 root wheel 893 Jan 8 07:38 '/macOS Install Data/Locked Files/.disk_label'
-rw-r--r-- 1 root wheel 15 Jan 8 07:38 '/macOS Install Data/Locked Files/.disk_label.contentDetails'
-rw-r--r-- 1 root wheel 3557 Jan 8 07:38 '/macOS Install Data/Locked Files/.disk_label_2x'
-rwxr-xr-x 1 root wheel 23520 Dec 1 12:37 '/macOS Install Data/Locked Files/cleanup_installer'
-rw-r--r-- 1 user staff 269647 May 17 2017 '/macOS Install Data/OSX_10_13_IncompatibleAppList.pkg'
Then, copy the download directory off to another machine for future use.