In your case the the technician makes the other variable 1.5 when attack > 60. And when getting a STAB bonus, the stab variable is replaced by 1.5. So in your case STAB and technician should stack according to the information found from bulbapedia.

Does fury cutter stack with technician?

First use: Fury Cutter has 40 base power, and STAB and Technician apply. 40 x 1.5 x 1.5 = 90 power. Second consecutive use: Fury Cutter has 80 base power. STAB applies, but Technician does not.

Does Choice Band affect technician?

40 + 50% for Technician is 60, and then adding 50% on top of that for STAB brings it to 90. The choice band doesn't increase the base power of the move, but rather effectively increases the pokemon attack stat.