What ratio of bicarb to vinegar do I need in order for the result to be pH neutral?
Your calculation is correct (14.3 grams of 5% acetic acid completely reacts with 1 g sodium bicarbonate). But you're not interested really in "completely reacts"; you want something like pH 7.

You've got it just about right with your mix; you're at the endpoint, and this is a point where the pH will drop very rapidly with even a small addition of vinegar. So it would only take a few additional drops to make the pH go down to 7... but that may not be what you really want.

Sodium acetate has a mild salty taste by itself. So I'm not sure adding extra vinegar will be worthwhile, it'll make it a bit more vinegary.

Here's what I'd do: Mix vinegar and baking soda in the ratio you've figured out, and then see how that tastes. Make adjustments at that point according to taste, rather than by "titrating" to an arbitrary pH.