This answer doesn't distinct between how STAB is considered and how Technician is considered. The Fury Cutter example where the base power exceeds 60 has nothing to do with STAB itself.
It's not accurate to represent STAB as a modifier to base power. STAB is one of several factors considered *after* the initial damage amount is calculated and base power is considered. This is one way to explain why Technician's effectiveness is not affected by STAB.
Applying STAB boosts to base power is useful as a way to compare and approximate damage, but it's not actually what the game does.