I think I did it like you described (but this was on the older tax forms as my one with taxable scholarships graduated in 2018). I think I used Turbo Tax for mine the last 2 years, and it asked what was on the 1098T, asked if that was correct, I said no, and then put in the numbers like you described. You have to do a little more adjusting with the numbers as you have things not on the 1098T like books and supplies, but it works.
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