I have only been charged once for my foilboard and it was a trip to Belize where surfboards are not commonly taken.
If I remember correctly, most US based airlines have certain destinations that surfboards are acceptable as one piece of luggage.
I ended up with the FBC wing v2 Small (165x75cm) it’s a bit big in general, but the smallest width that can fit these foils. With padding it is a tight fit.
Oth the setup works, 23kg with all the gear shown. The bag is very bulky but not a complete nightmare (3 flights later), and no damage so far.
I added a green plastic garden tray to protect the “bottom”, and cardboard and wetsuits etc to add padding. The padding of the bag is pretty good. Because the board and foils are small, I used a strap around the bag to take out the excess to prevent everything moving around
An improvement on all of this would be a rigid plastic plate or box or something that the foils mount onto and then just put that setup into the bag.
The 31" width is sufficient. I can vouch for this bag, working out well for me, more durable than my Manera wing bag.
Thats the same bag I’ve been using with my AFS gear for the past 9 months and I love it.