I think that there is zero harm in exploring refinancing. The only downside is a very temporary credit score ding for the pull, but unless you are planning on a major house purchase in the next few years, its nothing to concern yourself over.
So poke around. If you get a lower offer, I would take it, and then you have bought yourself the time/flexibility to decide how you want to best pay off the loans. You can ALWAYS pay off your loans in full, whether it is Jan 1, a few months after that, or a few years after that. But I suggest exploring if there is a way you can extend your time and be able to use your money for investment opportunities that you would otherwise miss out on (IRA contributions for the year is nothing to sneeze at). This of course is contingent on your confidence that you would invest your money instead of frittering it away!
I don't know how recent of stories you are looking for, but I refinanced my loans through Earnest 3 years ago. They have been a dream to work with. Zero complaints. I got a fixed rate of under 5%, which tipped the scales towards investing instead of paying them off. Now, we have built enough assets to pay off the loans many times over, and I am content to continue this way. I know that if the day ever comes that I can't stand having debt, I can wipe them out in a few hours. But I don't NEED to yet.
I will say that my rate did change only slightly between the initial quote and the actual real pull. The first is just a pretty good guestimate, but the pull gives them actual data and information about you to base on. So I would expect the end rate to change a bit. But the quote was pretty close to the end rate so I didn't mind.
Like I said - you won't hurt anything by seeing if you can find a better rate... you are keeping your financial options open. You don't have to take the refinance offer if it doesn't suit you, and you have a good fall back option of wiping them out next month. You're in good shape either way you slice it. You just have to decide whether you want to optimize for the math or for the feeling of debt freedom. I personally went for the math and am *really* glad for it now, 3 years on.