Fake out is too good not to use. You'd need another poké to handle the rock/steel/ghosts but otherwise the tech and STAB boost to base 90 really softens some pokémon up. With a focus sash, you can switch it back in with no fear (discounting the uncommon Sstorm/stealth rock etc.), unleash another fake out and continue sweeping. As a revenge killer, it also gets that free attack with fake out so it may be considerable alongside a bulky pokémon with explosion to give it a free switch in.
Would Scyther be more useful to use technician however? Aerial ace is certainly a considerable option versus the double teamers and random brightpowders.
As for the initial question, it shouldn't matter which order you apply multipliers. You can just multiply the multipliers by the initial power. STAB, tech boost, choice band, critical hit, resistance are all interchangable. At 1.5, 1.5, 1.5, 2 and 0.5 their product is 3.375 which can then be multiplied by the initial base power.