<human>: Can you summarize the given text in a few sentences?

I have a private student loan that was originated through Citibank years ago. It recently got sold to Discover. It was a 30-year $40,000 loan. The monthly payment is $325. So far it's been churning for years and the total balance is still above $40,000.

I called Discover to ask about refinancing the loan or getting a new (shorter) loan term. They said they bought a bunch of loans from Citi and frankly didn't have anything to offer. They even suggested finding another bank who could offer a better value and taking the loan over to someone else. 

I feel like at this point the best option would be to make a lump-sum payment (probably $10,000) and then refinance the balance into a 15-year loan with roughly the same $300ish monthly payment. I have enough in savings to make the lump sum payment and over the length of the loan this will save tens of thousands of dollars. 

Two questions: 1) does this seem like the best course of action? 2) which banks even offer something like this? My preliminary research and phone calls have turned up bupkis. Most banks don't seem to want to deal with private student loans.
<bot>: I have a 30-year, $40k private student loan; and want to make a $10k lump sum payment and refinance to a 15-year loan. Which banks can do this?