I work in the mortgage industry, see credit reports every day. Short answer as previous posters have said––there's probably no way you can get a discount off what you and the wife owe. If you're concerned about your credit score, you do NOT want a stafford loan to go into default. For all mortgages, it's generally a big reg flag to have delinquencies on govt debt. Plus, each month you don't pay, it'll probably hit you for 5-15 pts. Then the collection (or settling for less than you owe, which shows up as "charge-off/loss) alone will probably hit another 20-30 off.
What you CAN do, is write two checks, and pay down the principal balance, so you pay much less in interest. Basically, in this case, you're speeding up repayment.
the first check for the minimum, required loan amount.
The second one for whatever you're going to put towards paying it off. Make sure 1) you write in memo field "Apply full amount directly to principal on loan # xyzxyz," and take a photo of it, just to be safe. then send it certified mail. That way you've CYA and can document if any dispute arises. Sometimes, mortgage companies take extra payments and aply them into the future (ie, you pay extra for a few months and they view it as you pre-paying a few months ahead).
So, say you're willing to drop 5500 onto the loan, min payment is, say, 200. Write one check for 200, and then write another one for 5500.
What this will do is lower the amount of the monthly payment that goes toward interest, which means more goes towards principal (amount owed), meaning the balance on the loans go down a lot faster. Paying less interest = good.
So, unfortunately, probably no quick fix, but if you drop the cash up front, you can really speed up the repayment.
Hope this helps