Being a decent British citizen hardly ever leaving my quiet home town even on holidays,from 1998 to 2001 I ..... in Moscow

Правильный вариант - had been living.

From 1998 to 2001 I had been living in Moscow as I had been invited to teach English in Moscow State University.

Мы употребляем Past Perfect Continuous, так это был длительный процесс, который происходил определенный отрезок времени. Кроме того, from...to... является тайм маркером Past Perfect Continuous.