The answer to your question is no. You cannot work only 6 years and still get your loans forgiven under PSLF.
I would pay off more than the PSLF amount even if I were planning on using for many reasons. 6.8% interest, right? There is basically no reason to believe the market will return substantially more than that consistently after inflation.
1) You plan on working in public interest for 120 payment periods. But, people get fired, take time off, get laid off, budgets cut, hate their job, become stay at home parents. etc. If you work in public service for 119 months you get 0% forgiveness. So, there is no guarantee. Congress could get rid of that tomorrow if they wanted to show up to work to do it. If you can afford to pay more, you reduce the interest you'll pay in the case where your plan doesn't happen for some reason.
2) If your plan goes exactly right and you work 10 years, then you get $250,000 forgiven. My understanding is this was income that is taxable, though maybe that is different between IBR and PSLF. If it is taxable, the tax on it is like $60,000 if your income is already $110,000 a year. If by waiting and paying slower you pay $57,000 payments (mostly interest), and $60,000 in taxes, you might not be saving as much as you think when compared with your ability to right now just pay the $160,000 off.
3) I am going to assume you are young, single, and childless. One of those is guaranteed to change, and the other two probably will. If, right now, by working hard you can be debt free in 2 years, you might find that you would prefer to work only 40 hours a week for 9 years instead of 60 hours for 6 years in order to spend time with a spouse or child or even the couch! You might find that you can't retire in 6 years anyway because you now need more than $17,000 a year to support your family. Once you don't have the loan, you have a lot of freedom.
4) In your specific situation you are asking us if you should work an additional 4 years of your life to save approximately $90,000 on your loans. In 1 additional year of working, you could fully pay off the loan. Therefore, if your goal is to work as few years as possible, you should pay of the loan and work 7 years instead of 6 v. working 10 years and not paying off the loan. I guess if your primary goal is to not pay for school then working 4 years to avoid paying the remaining $90,000 in loans at the end is fine. But that's a dumb goal.