Floating-point arithmetic... (=SUM) doesn't work correctly for my basic decimal numbers

Here are 3 options, only one of which works. It STILL involves rounding. that is INEVITABLE. Since I had no idea where your numbers came from, I made up my own set (of 38 numbers). Nineteen positive numbers and the same 19 numbers multiplied by -1. So I KNEW that the sum was zero.

Simply summing them, as we already knew (Option 1) doesn't work. Surprisingly (to me) Option 3 (use an array formula ro round them and then sum them) didn't work either. However, the rounding option that I have been suggesting does work:

=ROUND(SUM($A$3:$A$41),3)

If that isn't good enough for you, then I think you need to explain clearly why it does not suit.