There is no way to fix the self-reference issue. In fact, self-reference screws up large portions of ‘nice’ results in mathematics — the famous Godel Incompleteness Theorems are effectively applications of self-referential meta-statements.
I am NOT saying Zeno is right. I am not making any comment on the paradox at all. We could discuss that issue at length, and still not reach any conclusion. I am simply describing the way mathematics works.
You are welcome to be a finitist. You are in the minority, and limiting yourself mathematically if you do, but you can. This doesn’t change the fact that your other arguments are wrong from the mathematical perspective. You can’t just sit back and say “I’m a finitist, so calculus is wrong.” Calculus is a self-contained theory, which is true from its own starting points. Any finitist theory will be true from its starting points. Neither invalidates the other.
Study “non-standard analysis” sometime. A proper treatment of the work done by Robinson should make this clear.