An intermediate approach I've been taking with my own son is to use calculus and initially not bother with either the manipulation OR the formalism. You have something moving, have the position and want the speed. Or vice-versa. You use it in a bunch of places to build out vocabulary and fluency, and build up both the mechanics and the formalism later.
And we derive a few formulas along the way. integrals of x and derivatives of x2 (x^2, depending on your programming language) pop up all over the place.
I don’t know how old your son is but for a high level and amusingly written book was How to Ace Calculus, The Streetwise Guide. I know it sounds a bit gimmicky but even after years of calculus classes I found it helpful for the higher level view. I always found from engineering school there being a stark difference between the classes taught by engineers and those taught by mathematicians. It always made more sense to me to have a concrete example of why I might use something before diving in than to have all this abstraction and be expected to abstract it to other problems.
And we derive a few formulas along the way. integrals of x and derivatives of x2 (x^2, depending on your programming language) pop up all over the place.