Comment by meindnoch

>I'm sure there's some fancy mathematical trick that would just do it. If I were only more comfortable with math... my handwavy sketch would be to compute the speed function by differentiating the formulas to get dx, dy, and dz and passing them through the Pythagorean equation, then reparameterize on a t' variable using the inverse of the speed function? Maybe? I feel like I'm speaking using words I don't understand.

What you're looking for is called arc length parameterization. Basically, you need to compose the curve with the inverse of its arc length function. Aside from a few special curve families, closed-form solutions don't exist.