You are playing with fire. Just because you rename a column, Manager does not treat the contents as anything different from what they were before. You may be able to force an invoice to look like what you want, but you are effectively using Manager as a word processing program when you do that. All the accounting operations happen exactly as they did previously. You have just put a new name on a display. The risk that your records are horribly incorrect is extremely high.
To answer your direct question, there is no way to inject a custom field into a line item, because they are in no way connected. The custom field is at the record level, not the line item level.