I think this is a matter of time.
One of my current baby cried loudly when she first started. She came in April when she was 11 months old. Although I've had this situation before, never in the past has it continued for as long as it did with this little one.
She screamed every time I put her down and she became absolutely hysterical if I left the room even though my home is open plan and she could still see me. Her grandmother picks her up from here at the end of the day until parents finish work, and even she was dealing with the same issue.
I never, ever, pick up new children just for crying. If they are hurt or have reason to be upset, that's different but not for crying to be picked up - and this little one would stop the second she was picked up to be carried into the dining room for lunch/snack and scream again the second she was placed in the high chair.
I'll admit, it was rough. Knowing the grandmother was dealing with the same issue did help some. Initially, every time she started crying, she would set off all the others but gradually even they tuned her out. Like yours, she would grin at me periodically but the crying was more common.
I had discussions with the Mom who claimed that they didn't carry her around all the time at home (I'm still not convinced that was true - but feel the Dad was the biggest culprit because if she so much as squeaks or pouts, he fawns all over her).
It took until 2 months ago for her to stop so a full three months of her in full-time care. Now she is happy and one of the biggest personalities in the group. She still has her melt-downs but they are much better. They now only happen if an unfamiliar Dad picks up or drops of their child - the unfamiliar Moms don't seem to bother her. It still happens if we have a play date with another carer and that other carer gets closer to her than I am.
One thing I did have to do - after discussion and agreement from her Mom - was once she became hysterical, to place her in her crib - until she'd either calmed down through exhaustion or fallen asleep for a little while. That certainly helped to have that option as a last resort, if only for the others to have a bit of a break from her hysteria.