See this script I developed: MarTech/UTM-Tracking at master · yanirclsr/MarTech · GitHub
Besides storing the original and last UTM params, it also stores the original and last referral in the cookies (or local storage).
You can then capture them into your forms very easily.
Feel free to comment here if you need further help.
This is very interesting. How would this collect the UTM tracking of the newer formats such as the advanced tracking in AdWords?