What this calculation shows is what glide ratio Godwit must have if it spends 1/3 of its body weight very efficiently to gain altitude and reaches destination in completely calm air. By the looks of it it doesn’t have this glide ratio, and I doubt it spends 1/3 of its weight only gaining altitude.
So it means that it must gain altitude and, perhaps, travel speed by alternative means, most likely using updrafts and riding winds.
Your calculation is interesting, but I beg you to go outside and look at how Godwits actually fly. Godwits fly in a straight line using rapid powerful nonstop flaps. They are relatively heavy birds with high "wing loading ratio" and their entire body plan is hyper-optimized for this type of flight and no other. This is especially true during migration when they accumulate lots of fat and their wing loading ratio is particularly unfavorable for soaring. Godwits are among the fastest-flying birds in a straight line, and they have never been observed to engage in any other mode of flight, nor can they. They cannot use regular soaring. They cannot use dynamic soaring. They do not fly like seagulls. Their wing area is simply too small to allow any other type of flight. They also typically do not wait for favorable wind to fly. They just take off and go.
I agree with your points. What this calculation shows that godwits must rely on favorable winds and updrafts (which benefit any flying object, including birds, since motion is relative); if this is not the case, they just not going to reach claimed distances given their weight and how much fat they are carrying.
So it means that it must gain altitude and, perhaps, travel speed by alternative means, most likely using updrafts and riding winds.