Yes, that is fundamentally correct. TurboTax is capable of handling it all, but the interview is complicated. I recommend using some short cuts.
1. You will use $4000 of the expenses to claim the AOTC.
The simplest thing is to modified the 1098-T. I would enter $4000 in box 1 and leave box 5 blank. Lying to TurboTax to get it to do what you want does not constitute lying to the IRS. Don't enter any other numbers.
2. You student will declare the $1740 scholarship to be reportable income, freeing up more expenses for the ESA distribution.
Does your student have any other income? That is, if it wasn't for having to report the scholarship and 1099-Q, would he even have to file a tax return? The shortest short cut is for him to not file a tax return, at all. We don't know exactly how much of the 1099-Q will be taxable, but I'm pretty sure it will be under the $350 filing requirement (assuming we use the $2300 board allowance). That said, some people recommend you file anyway, to document the fact that he is counting the scholarship as income (allowing you to claim the AOTC).
3. We need to determine the taxable portion of the ESA.
You have $6354 tuition + $300 books + $2300 board = $8954 Total expenses less $4000 used for the AOTC = $4954. That is only $45 less than the $4999 ESA distribution. Using your basis fraction, that works out to $42 taxable. I think that's small enough to ignore, since it won't actually get taxed (his standard deduction covers it).
If you do deicide to have your student file and need instructions on a short cut entry method, let me know.
