You explained it yourself!

Fusing 1.2 million tons/second of hydrogen nuclei represents a heck of an increase in thermodynamic entropy - far faster than any reverse of entropy that is occurring due to any evolutionary activities here.

Remember, a SYSTEM must increase in entropy. In this case, the Earth cannot be considered a closed thermodynamic system; the Sun is also a part of that system. So, you can have evolution, and not come close violating the second law.

You are confusing increased order with decreased entropy, but there are examples of non-biological systems that tend toward spontaneous order (galaxies, solar systems, etc.) that don't violate the second law.