Use the option SaveDefinitions -> True. This saves the definitions of the functions that are used explicitly in the body of Manipulate; the remaining function definitions should be moved inside the body of Manipulate to be recorded.
SaveDefinitions -> True
Manipulate
Jon, here is an alternative to Gianlucas solution:
InitializationCellEvaluation
True
Your notebook with these modifications is attached
Perfect, thank you!
Awesome, thanks!!