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Is this a federal student loan? I think some, but maybe not all (?), state-issued loans are federally backed. You can find out by going to the National Student Loan Data System (nslds.ed.gov) and seeing if the loan is listed there.
If it is listed there, rehab will work for you the same way it has with other people on these boards - you make 9 months of on-time payments and then the loan is sold to a new servicer and regular repayment resumes as if you'd never defaulted. The new tradeline is back-dated to the original open date of the loan, giving you a positive tradeline that boosts your score.
The payments you make in rehab may initially go to interest or fees that you owe, but should not just be paid to the CA as a "fee" for their services. Those payments may not decrease your principal at all though.
If you don't want the loan to be sold again, your only option is to pay off the CA. If you can do so with a lump sum and just want to be done with it, you should be able to do that, but it won't help your credit nearly as much as going through rehab. You should also know that federal loans will follow you forever, are very hard to discharge in bankruptcy, and the CA could garnish your wages or even Social Security payments without getting a judgment. Those are all great reasons to pursue rehab and get out of default.