To my knowledge it is only possible to have a second mortgage stripped if the value of the first mortgage exceeds the value of the property.

I believe you should look into loan modification or short sale. Loan modification is possible if you can demonstrate the financial ability to pay lower payments, but often banks are not very willing to consider loan mod until after a foreclosure action is filed. Short sale may be an option if you just want to break even on the whole deal and are willing to lose the house. If you can find a buyer who will pay the actual, current market value of the property, and you can demonstrate financial hardship, you can bring the offer to the bank.

Bankruptcy may also be an option for you, but I don't believe it would reduce the amount you owe on the mortgages.

You really need to see an attorney to discuss all your current financial situation and the options which may be available to you. Most offer a free consultation.

You need to determine which mortgage loan is the senior loan, and also confirm whether the loan is secured by business or personal assets other than the home.

A second loan, if the sole security is a primary residence, can only be "stripped" (treated as wholly unsecured) if the amount of the senior loan exceeds the value of the house and there is $0 value to secure the second loan.

If the smaller loan is in first position and the home is the sole security for the loan, you cannot modify either loan because the value of the property ($300k) exceeds the amount of the first loan ($64k), and there is therefore some value in the property that secures the second loan.

If the larger loan is in senior position, then you can strip the entire $64k loan because the amount of the first loan ($344k) exceeds the value of the property ($300k).

FYI, you cannot modify a first mortgage loan at all on a primary residence.

Note that if (a) the property is not a primary residence or (b) there are assets other than the house which serve as security for the loan (such as a car or business assets), then you could "cram down" the loans to the value of the value of the property ($300k) no matter which loan was senior.