Must one remain in the lavatory until the urine completely stops, or is it sufficient to ensure its momentary cessation and disregard subsequent drops, given the hardship and embarrassment this causes?

Whoever experiences drops of urine after ablution must perform istibra' (pelvic floor exercises to ensure no urine remains) before prayer, allowing enough time to pray with the congregation. If he is unable to do so, there is no sin in missing the congregational prayer. A mere sensation without certainty has no effect. If he sees something, he should repeat istinja' (washing the private parts), wash whatever was affected, and perform ablution again. Otherwise, nothing is required of him. He should be patient, seek reward from Allah, supplicate, and consult a specialized doctor.