How to move text up/down in Notes using keyboard shortcut?
This should be possible using Cocoa bindings - see this answer:

https://superuser.com/a/283948/659069

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The example below (taken from the link above) binds a 'move line down' shortcut to Opt-DownArrow - you should be able to modify this to meet your needs.

Create the file ~/Library/Keybindings/DefaultKeyBinding.dict and enter the following:

{
    "~\UF701" = (
        "moveToBeginningOfLine:",
        "deleteToEndOfLine:",
        "deleteForward:",
        "moveDown:",
        "yank:",
        "insertNewline:",
        "moveUp:"
    );
}


This will add the shortcut Opt-DownArrow for a line-swap command (with the line below) to every application supporting the Cocoa text system.