Can I exchange my $4000 Tuition and Fees Deduction for American Opportunity Credit of $1000, as this would benefit me more (seeing as I don't owe taxes this year)?

Use the "tools" search topics for "letme" (without the quotes)  to select the credit you want.

TurboTax should select the method that is most beneficial.

You're probably not eligible for the American Opportunity Credit (AOTC).

 A full time, unmarried student, under age 24, even if you don't qualify as a dependent, is only eligible for the refundable portion (the $1000) of the American Opportunity Credit if he supports himself by working. You cannot be supporting yourself on parental support, 529 plans or student loans & grants. You usually must have actually paid tuition, not had it paid by scholarships & grants.  It is usually best if the parent claims that credit. 

If you are eligible, you have answered  something wrong, in the interview. But, a lot of people are just not eligible. See https://www.irs.gov/Individuals/AOTC

https://www.irs.gov/newsroom/american-opportunity-tax-credit-questions-and-answers

To try to change it: Type letme (no space between let & me) in the search box. When the dropdown list appears, click on letme rather than "jump to letme'. On the next drop down, click on the "jump to letme” link.