If your transatlantic carrier is not US-based, it's likely there is no flat tire rule and you forfeit the value of your ticket and all remaining legs including the return the moment the doors close. No credit from your missed flight. New funds only at walk-up full fare.
I've seen this scenario blow up with a one-hour trip from San Jose, CA to LAX in the morning to catch a transpacific flight with no flat tire rule. The desperate attempt to save the transpacific ticket from being forfeit is to fly WN to another LA area airport and fight through the bad LA traffic to make it to LAX before check-in closes and no further bags accepted.
This year has not been good for Southwest regarding cancellations and delays.
Your trip is late July, so you have time to make a decision on whether to go forward with your plan or change it.