I couldn't taper. Not saying no one can. I just found it difficult to keep to the lower amounts.
You're at an advantage in that you already had the discussion with your doctor, so you could just go to him, explain your fears of increased anxiety in withdrawals so he can give you the appropriate meds so you can get through work and the business trip more easily: then just quit.
Guaranteed your drinking is doing as much or more damage to your liver than benzos for 4-7 days, once it's our of your system you'll no longer need them.
Then you won't be missing gym workouts anymore! (Can relate to missing the gym after drinking....)