When I was younger, I was in a similar situation to yours. Though time has passed and that is fortunately now behind me. So, I understand how it feels to be looking at such a huge number, and the anticipated relief of becoming debt free. However, I believe it is better to be rational rather than emotional in money matters. So, ...
According to my loan calculator, a loan with of $280k in which you will pay back $396k over 25 years must have an interest rate of slightly less than 3%. Even today, that is pretty cheap money. In addition, student loan interest is often tax deductible (check your tax situation), making the effective interest rate even lower.
I would compare the cost of any money that you divert from other things to pay off the loan faster, including opportunity cost. (You could be very close to the rate of inflation, which means just sitting on $280k in cash could cost you as much.) For example, it would almost certainly make more sense to pay off consumer debt first. (I always focus on paying the highest interest loans first.) Your mortgage is probably low interest and potentially tax deductible, but is it as good as the student loan. Can you invest in opportunities that have a greater return? I would put these before low interest debt. (I had multiple student loans with different interest rates, so I tracked them separately. I track ALL my debts in a spreadsheet and sort by the cost (interest - tax benefit, if any).)
As Karen said above, I would make contributions to 401k -- especially those that are matched. (I did.) My employer matched 50 cents on the dollar to a certain amount, so I made 50% return immediately. Your employer might even be better. Pre-tax contributions also reduce your taxable income -- saving taxes and helping keep you below certain income-related cutoffs.
I treated the money I paid toward my student loan debt and 401k as if I never earned it, starting as close to my first day of work as possible. That way I never missed it. (I advise my grown children to do the same.) I did my best to scale my life-style within the remaining income. (This also led to a little boost in spendable income when I finally paid off the student loans.) All of this assumes that you can still buy groceries and gas with the money you have left.
Re-evaluate as life situations change. For example, you said your repayment plan is income based. This could change the cost of the loan as your income increases -- the interest rate my go up, but the tax benefit may also increase as your marginal tax rate increases. (My daughter's student loan repayment was not income-based, but it was variable rate, so money she borrowed at an initial rate of ~ 5% went up to 12% over a short period. This changed the payoff priority considerably.)
Finally, I would ignore the possibility of having the loan forgiven until it happens. This might cause a new kind of problem when it happens anyway, as Karen said.
My two cents, based on my experience... I hope it helps.