Check what possible alternative routings you have to get you home today. Primarily using Lufthansa group options as you're more likely to get them to do so. After that look at any Star Alliance options, as EW is a Star Alliance affiliate. But they won't potentially put you on another routing until it's obvious you will miss your connection/last EW flight to GOT.

If there is a nonstop option also have that info handy but as it most likely won't be on a Lufthansa group you may get push back on that.

Be reasonable but steadfast with the staff.

Also, if things really go south check routings first on EW and then on Lufthansa Group airlines for tomorrow incase so you get put on the flights that best fit your needs.