How to generate random values in range (-1, 1) such that the total sum is 0?
Since you are fine with the approach of generating lots of numbers and dividing by the sum, why not generate n/2 positive numbers divide by sum. Then generate n/2 negative numbers and divide by sum?
Want a random positive to negative mix? Randomly generate that mix randomly first then continue.
If the sum is 1, I could just divide the values by their sum. However, this approach is not applicable when the sum is 0. 
Maybe I could compute the opposite of each value I sample, so I would always have a pair of numbers, such that their sum is 0. However this approach reduces the "randomness" I would like to have in my random array.
Are there better approaches?
Edit: the array length can vary (from 3 to few hundreds), but it has to be fixed before sampling.