I think that both of these are grammatically correct. One emphasizes what has happened since a certain time and the other emphasizes what has happened because of a particular event or experience.
But I recently saw "As having been to America, she..." in a text book and I think it's incorrect, although I'm not exactly sure why. Also, would "Since having been to America, she..." be incorrect?
So far my efforts to find an answer to this have been fruitless. I hope someone here can help me! Thank- you.
Since she has been to America, she..."
"As she has been to America, she..."
These are both correct and mean what you say, although they could both also mean 'because she has been to America'. 'As having been' sounds wrong to me. We could use a gerund with 'since', but I'd probably use 'since going to America'.