HELOC rates should be close to prime (5.25%) if you have plenty of equity and a high credit score. Some are slightly below that (lowest we found was prime minus 0.3%).
Otherwise sounds like a good option to withdraw as you need it, especially as you wouldn’t want any assets to count against you for need based aid. A HELOC can enable you to have virtually no cash in your bank/savings account on the date you complete the FAFSA by temporarily paying off part of the loan with those savings.