Easy, if they're connected globally through fast trade: flu season.

Otherwise maybe it's bad luck to take bodies out of the morgue until it's past a certain date. The date can be connected to a fable. Not the healthiest idea, keeping bodies around, but still...

Third option: a ceremony can only occur in early autumn, such as a rite of maturity or a challenge of succession, that tends to leave behind a lot of bodies.

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.

Necroposting because all posting is necroposting if you're impatient enough.

Lilitika has very blatant Attic phonaesthetics (even with somewhat similar letter frequency tables) in its later dialects, but underneath it all, my actual induction into curiosity about constructed grammar came from a cursory awareness of the agglutinative habits of Korean case markers, so there's some resonance with that in Lilitika's early phases, which verge on polysynthetic. I did manage to get an almost 1:1 parse tree with the opening lines of the Iliad, though, since Lilitika essentially has the PIE cases. Best witnessed here.

Other conlangs on the go:

Ksreskézaian languages are a self-conscious effort to avoid mimicking anything of which I'm aware. However, due to contact with humans, some of the later forms do include a small amount of vocabulary with recognizable Terran roots.

Roshagil: Mandarin after a bad one-night stand with English. Though the vocabulary and near-total lack of morphology is unquestionably Chinese, the depredations of time have curiously restricted the language to the twenty-six letters of the English alphabet. Half a million years in the future, ASCII remains unchanged, though the letter forms are not very recognisable.

Kuanid: Not much of a start on this, but my hope is to eventually derive it from a boiled-down convergence of the procedural languages of the EU—so, mostly French and German. Luxembourgian, if you will, or Italo-Germanic more historically. This is the language spoken by most of the future-humans in the setting, and is notoriously described as having no standard form, but rather an immense sea of synonyms and graphemes that argolects and idiolects are plucked from. Consequently I've considered adding ideograms to Kuanid, but not to Roshagil. Yup.

Glissía: Attic. It's meticulously constructed out of Greek with some of the basic facts of PIE shuffled around for convenience and a formal syntax for symbolic logic grafted onto it. The language is spoken by inconceivably stodgy academics who refuse to change much about it. Originally the plan for Glissía was to find a happy medium between Latinists and Hellenists, a sort of hybrid that all Classicists could be proud of. Then the plan was to construct an absurdly complex superset of both Latin and Greek that could be mixed freeform. Now it's just Greek with extra declensions and cases.