Can you try selecting all text including the quotations and adjust the letter spacing wider, then select only the letters and adjust again in the opposite direction to less spacing? This works pretty well for me. Also, you might try using different fonts to see if that solves the problem. I also put the quotation marks in as they come out of my American English keyboard, (” = shift-option left bracket), (“ = option right-braket) then adjusted the first one down using a baseline shift. I am not sure if this is the cause for it looking better.
It’s a bit of an optical illusion, because the serif on the A is right next to the first quotation, while the serif of the h is far from the right quotation. That’s why you need to manually adjust it to make it look right.