Google search for "how to talk to a live person at [shipping company] "
Even if you somehow press the wrong call direct digit(s), having your call redirected to the right department or person is not difficult. Usually it's just customer service. I've also spoken to FedEx reps who deal with collecting taxes and duties payments for parcels over the phone about this kind of thing long ago- details about my parcel; handle with care etc.
So right after paying them...
They can redirect your call in priority order quickly; to have someone "leave a note" so to speak. And honestly, it works. Like I've said before in a previous post, I've had delivery drivers ask: so this is an important parcel, right... a milestone birthday gift?? Because that message got passed on. Arrived without issues/damage and on time or even before time!!! They will send out their best people to make a successful delivery if you make that request.
You can also call an authorized ship center / their warehouse (one that is close to you and where the package will be waiting before being delivered to you). While you might not be able to control how well the parcel is handled step-by-step from a distant country, you can get local shipping centres to listen to you.
In my experience, this has worked for FedEX, UPS, and DHL. I can't say it will work for every shipping company. I'd rather not provide incorrect information.
Long story short - while meeting quotas is certainly vital for them; keep in mind that they are in constant competition with all the other shipping companies! They want your repeat business...like any other business you can think of.
For local businesses I just talk to the owner on the phone directly and/or in person if I'm buying that day. They assure me that their senior delivery drivers will deliver something (like a dining table or something fragile). A lot of rookie delivery drivers (especially those that are just looking to make ends meet) are often careless.
All the best.