Where would you rather invest your time? Upfront to try and come up with a more accurate estimate, or throughout the project to manage around an inaccurate estimate?
In other words, what would you prefer? A good estimate paired with a flawed project management process or a poor estimate together with a robust process?
Coming up with good estimates is something that we all should work to get better, but we need to make peace with the fact that there's no such thing as "a perfect estimate," and the only solution to an imperfect estimate is a strong process to manage projects.
That's what I'd do: invest as much as possible into building a strong project management foundation that helps navigate our imperfect estimates. This formula will certainly win every time.