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With all due respect, the way to gain control of the situation is to file the 7, wait for a discharge and then file a ch 13 to create a payment plan. All that will be left will be the house, student loans if you have them and other non-discharged debt. The house heloc will have a zero balance but there will still be a lien on the house from it. In order to void the lean, the first loan has to be greater than the balance due, which you say is true. The ch 13 allows you to avoid the lien and never see it again as long as you finish your plan in the 3 to 5 year time period. If you don't keep up with your payments, them you're back to pre-13 status.
If you put yourself at the mercy of the bank, having both a 1st and second loan then you will have many sleepless nights wondering if they will accept your modification and then you might end up with a deficiency judgment and that could happen any time. Heck, the bank could sell it to some collection agency for 10 cents on the dollar and come after you for the full amount. Of course they'll wait until you've built up some equity down the road.
I am not an attorney but I've just gone down this road. Started in Aug of 2008 hoping the banks would help. Not gonna happen! The only thing I have to say is that I wish I had faced reality and filed a year sooner. My retirement accounts would still be intact and I would recover much more quickly.
Best of luck to you and your family.