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Also, I would never file for BK, even if it were an option.
in that case, your only chance is time. They may be lumped together for repayment, but it is still 11 accounts that went into default. With the gov't backed loans you can rehab them and they remove the negative info, but not the case in this one. You may be looking at 2+ years before they are willing to do a loan. Also, if you are in a payment agreement, you want to have it in writing as a verbal on eover the phone will not usually suffice to an LO/UW. They will need proof of the payment plan and the payments made under it, or they will require PIF.
Just an idea -- after making on time payments for a year or so, Id approach the bank and ask if they would remove the default status. It never hurts to try. They may be more willing to work with you once you prove you pay on time. Most of the people on this board are here because they had some sort of credit mishap in the past -- just work on repairing and then look into buying down the road. Who knows what the mortgage industry will bring in a year... hard to tell.