How can we reconcile the fact that lunar and solar eclipses are signs from God meant to instill fear due to the poor state of the Ummah, with the possibility of predicting their occurrence astronomically for years to come?

Eclipses (solar and lunar) are two of Allah's signs, by which He instills fear in His servants. Knowing their timing through calculation does not contradict this. An eclipse may be a cause for something fearful, and the Prophet, peace and blessings be upon him, legislated at its occurrence the eclipse prayer, charity, supplication, and seeking forgiveness to avert punishment. As for the claim that eclipses occur when the condition of the Ummah is bad, this has not been authentically reported in the Hadith, for the sun eclipsed during the lifetime of the Prophet, peace and blessings be upon him, and the condition of the Ummah was not bad at that time.