(I think the difference between the OP's calculation and my estimate all comes from their 80% efficiency vs. my assumption of 100%. My 'roughly' twice as far as

(I think the difference between the OP's calculation and my estimate all comes from their 80% efficiency vs. my assumption of 100%. My 'roughly' twice as far as high is actually exact under ideal assumptions. Where the slope of the inverted parabola is -1, the chord is 4 times the height, but in this parabola only half of the launch energy goes into upward motion, accounting for the other factor of 2.)