Will this work? Using litigation firm to resolve short sale negotiation over HELOC?

You're wasting another $3,000. The reason they will not give you any sort of guarantee is that they cannot sue your HELOC lender to cause any sort of settlement. Your HELOC loan contract is legal and binding, and the lender involved has every right to refuse to take less than is owed. There is nothing those attorneys can do to force that to change. They can only do what YOU have done, and that is to attempt to negotiate a settlement. There is no litigation involved, since they have no legal basis for suit. Understand, as well, that your HELOC IS a secured loan. Your house is the collateral.