Why does increasing the space constant increase conduction velocity in myelinated neurons if nodes of Ranvier are constantly spaced?

I think the simplest answer to your question is that you're correct in thinking passive flow would be what changes, but the reason behind it is important to understand.

I'd recommend looking at UT Health's neuroscience online resource where they break down action potential propagation in an understandable way. The main takeaway is that the space constant is determined by a number of different physical characteristics of the neuron/axon. You can find these characteristics at the link I provided, but the three parameters that define the length constant are diameter of the axon (d), membrane resistance (Rm), and axial resistance (Ra).

Starting with Rm (because you allude to myelin in the question), this is dramatically affected by myelination. An internode (the myelinated portion of an axon in between nodes of Ranvier) has an excessively high Rm, which just means that current doesn't readily flow across the membrane, so current doesn't "leak out" while it's passively flowing down the axon here. Therefore, increasing Rm by lengthening internodes would help increase the distance across which current can passively flow in the axon (which increases the space constant). Shortening internodes would have the opposite effect. However, you seem to be asking "All things with myelin remaining the same, why would a higher space constant increase conduction velocity?" That's where d and Ra come in. I explain these below:

The values of d and Ra are somewhat linked. Basically, a high the value of d allows passive current to flow more easily along the axon, meaning it has a low value of Ra. So in the context of your question, if you had an axon and theoretically doubled the axon diameter (so from d to 2d), Ra is cut in half (so from Ra to Ra/2) and passive conduction can speed up. This would increase the space constant by its effect on passive conduction. The converse is true if you shrink the axon diameter. However, it's important to realize that Ra can also be affected by other factors like the contents of the cytoplasm in the axon. That is why both are used to calculate the space constant even though they relate to one another.