Don't assume we need astronomy (at least as we know it) to give astrology to a flat planet.
There is no reason that astronomical motion has to resemble a circle in any way.
Cyclical functions are much easier to work with (don't start with anything too alien), but they aren't strictly necessary or even particularly important.
You
can just say that the star of Armok is aligned every 1000 days.
Individually, no astral event should be world ending. The combination of two effects should be fairly noteworthy. Three events with similar effects, occurring at once should be cause for concern, particularly if your astrologer failed to predict it, and you don't know where all these wild elementals came from, or what they want. All the stars must be right before C'thul'hu awakens in Ry'leh.
This makes even a weak, infrequent influence important, since it can join up with other effects for more potency.
I propose that astrology use and additive percentage system. Using my old example, water buys the full moon, the month of Felsite and some infrequent, but fairly potent planet. Say these have values of +6%, +9% and +7%, respectively:
All of Felsite is 109% as watery as normal. Expect spring flooding to be worse than normal on this planet.
Every month, including Felsite, there's a full moon. The two effects combine for 115% water. Presto, astrology can predict what day the annual frogman invasion will arrive (since the nasties presumably know when they'll have the advantage and strike then).
If, one year, the planet becomes dominant in Felsite (116%), the Frogmen invade twice, in the same month. A little extra surprise to keep you on your toes.
One year, water's planet becomes aligned with your world on the day of the frogman invasion. At 122% water, you can expect a lot more frogs than you planned on. On the bright side, a lot of masterwork booze get's made.
For events that can only happen during astrological events involving multiple bodies, simply don't add 100%. There's a 22% chance of water men coming out of the wells,
or whatever, at the same time you're trying to fend off this other ambush.
If astrological bodies with similar spheres are common (I'm assuming that a planet/moon phase/month combo, will be pretty rare), you'd want to have a minimum threshold of aligned bodies for certain distinctly astrological events.
You wouldn't want the system to be particularly potent, you'd just want it to be pervasive. My examples don't really reflect that, but activities from boosted spheres should get a small lift from the stars.
Creating an underlying system that effects all the random stuff in random ways would be great, since it actually makes the game feel less random.
Did that large group of trolls spawn because I was unlucky, or would a better astrologer have been able to help me prepare for it?
No longer do we curse the malevolent RNG, but instead we curse the fickle stars of dwarven fate.
More skilled astrologers should be able to recognize coming alignments sooner, or even predict how the world will react to them.