You can see here also that Y number for puzzle 69 is low

You're computing a number that is simply Y = sqrt(X) * 8192.
Where X is the normalized key position (from 0 to 1) in the puzzle space. What am I missing?

Nothing. It just needs more and more decimal places to get to a N-bit precision for the multiplication result. It's simply faster, and without losing any precision, to work directly in the original integer base.