Not not round enough balls to alter the data

Main answer

1. The balls were not, not round enough to alter the accuracy of the data.

The Original Poster's sentence is perfectly grammatical, although it is difficult to parse. In terms of punctuation (not grammar), the comma isn't really necessary and makes it a bit more difficult to parse, not less. The double negation is not the only factor here. If it was, the sentence wouldn't cause us any problems. The complicating factor is the not X enough to Y construction, which not only means that the thing was not overly X, but also that Y didn't happen. So there are three lots of negation involved here. We are dealing with triple negation!

There are a couple of solutions to to the OP's conundrum. They could, for example, lose one of the nots and use a negative prefix on the adjective:

2. The balls were not unround enough to alter the accuracy of the data.

This is still very clunky.

By far the most elegant solution is to lose the double negation and mark the non-finite clause as negative (using the less common X enough to Y version of the construction). As we saw before, in the not X enough to Y construction, the Y clause doesn't actually happen and is understood as negative even though it isn't overtly marked with not. However, in the X enough to Y version of the construction, the event in the Y clause ᴅᴏᴇs occur. Because the accuracy of the data was ɴᴏᴛ altered, we need to overtly mark the clause as negative:

3. The balls were round enough not to alter the accuracy of the data.

Perfect!

Notes on negation

Usually, if we had a sentence with two nots, we would expect to be able to paraphrase the sentence without any nots at all. We would let them effectively cancel each other out:

• I am not not helpful.
• I am helpful.

Here these two sentences mean the same thing, in the same way that the following formulas have the same values:

• -2 x -2 = 4
• 2 x 2 = 4

However, in the OP's case we have an original sentence with two nots and a paraphrase with one. This is extremely unusual given that none of the actual words have otherwise changed. The reason is that the logical form of the original sentence, example (1), is similar to:

• -2 x -2 x [-]2 = -8 (invisible negation for the last instance of 2)

If we cancel out two of the negations we get:

• 2 x 2 x -2 = 8 (where the last negation is now visible)

This formula is similar to example (3) above. In the same way that the last two formulae have the same values, so do examples (1) and (3)!