I think if you zealously stick to growing a conlang from roots, the result will invariably be an unwieldy kitchen sink of diachronics with no cohesion, simply because you can't really emulate the nuances, connotations, and settling that would manifest in a real population of speakers over a long period of time. So, supplement with some kind of vision. Sindarin and Quenya come to mind—they do have big sections of vocabulary that Tolkien built forward, from roots, but these were practicable because he had a strong, academic familiarity with natlangs from the families he was trying to emulate, so navigating the waters of consistency wasn't really an issue.

To go even further: in statistics, there's an algorithmic paradigm called expectation–maximization. The idea is that you alternate between calculating two sets of variables meant to reflect each other, typically by determining the expected assignments of data points to randomly-generated distributions, then determining the best estimate distribution (by maximizing model parameters) that would have produced those assignments. Substitute these estimates for the randomly-generated ones, and you can repeat the process indefinitely. For a wide range of useful models, the numbers will eventually converge to an optimum. Sort of like when you feed text into Google Translate repeatedly and it eventually finds a pair of phrases (or a small group) that it loops between. You can (and should) do this with conlanging, too, by re-deriving your original roots from the final dictionary to ensure they're consistent. It probably won't require multiple iterations, though.