Is there such a thing as a non amortized variable rate equity loan to 100% LTV?

This is an example of someone playing games with you or just plain ignorant of the facts. If a loan isn't amortized (paid down with each payment) it cannot be paid off. You would be paying interest only. The loan you are describing is an Adjustable Rate interest only loan which is not used by Lenders for parties in distress with their mortgage. A lender's Work Out department will usually offer a reduced rate fully amortizing 30 year loan with a payment that the borrower can afford based on current income and debt load. Your current lender is the first place to go.