OK, got it for "regular" homebrew (not Aurora unfortunately, so I'd still appreciate some help here).
Don't touch the XEX file itself - Any change will cause the app / game not to run (probably digital signature, checksum or something).
Launch Shortcut360 v1.1.7 and create a new shortcut.
Name: The app / game name. This is how it appears in the game list. Doesn't have to be accurate so you can change it if you want to customize.
Title ID: It is recommended to search xboxunity.net to see if there's a known title ID. Retail games will always have one, but homebrew might have one as well, decided by the community. If there is one, it is recommended that you use it to avoid clashes. If there isn't, just use a random one, but do search xboxunity to verify that nothing else uses it. It needs to be exactly 8 hex digits, so prefix with zeros if needed.
Icon: Optional PNG image exactly 64x64 pixels in size. If the game has a Title ID on xboxunity you can download the icon from there. You might need to resize it, which is easily done using MS Paint.
Media ID: For homebrew, this needs to be 00000000 (eight zeros).
Disc: For homebrew, both fields should be zero.
Path: Path to the XEX file to run, relative to the root of the HDD. Do not include the drive name and do not include a leading backslash. Use backslashes as directory separators. Forward slashes will not work.
Create your shortcut.
Go into the content folder, then to the title ID folder. You will see another folder named "00000000". Change it to "00080000".
Go into that folder. You'll see the shortcut file, and it will have the name of the app. Rename it to the title ID followed by "00000001", e.g. if the title ID is 12345678, name the file "1234567800000001".
Open the file in a hex editor. Go to position 0x344 (836). Look at the four bytes starting at that position. They should all be zeros. Change that to "00 08 00 00". Save the file.
Copy the content folder to your Xbox 360 and enjoy.