I could see this working out under one scenario, which includes all of the following:
a) you're over the student loan interest deduction cap
b) you get a lower APR on a HELOC with a fixed rate
c) you continue to make the same payments as before, regardless of what the new minimum is
In that scenario, you’ll end up saving a few dollars, will be more tax efficient, and won’t carry the loan for decades. But, I think the discipline required makes it far from a sure thing, and you’re probably better off just trying to increase your payments on your student loan to pay it down faster.