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No, that doesn't make sense. The more accurate gravitational acceleration is exactly what should make the calculus-derived number lower.
I just did the calculations using
Ship mass: 1.1*10^9 kg
Reach mass: 9.15*10^24 kg
G: 6.674*10^-11
Starting position: 7,636,500m from center of object
Ending position: 7,836,500m from center of object
My result was 2.24*10^15 joules. Which is only a bit less than the mgh value of ~2.39*10^15, and still a "healthy" .025kg of energy.