It's better to not use the abbreviated format of
%SingleLine% for text token variables – use
%Variable%SingleLine%. The former works but is not good practice, and Peter may very well make it more strict in future.
It seems to me that Jimmy's macro does exactly what you want except from a variable instead of a named clipboard (and with a minor embellishment).
When asking for help like this it's best to provide a complete working macro if possible. (The Keyboard Maestro share menu makes this easy.)
When people have a downloadable macro available to test they're more likely to help you.
The appended macro works for me. Give it a try and see if you can figure out what's wonky with yours.
Paste Each Line from a Named Clipboard.kmmacros (5.8 KB)