Like most things in life, it's a double edge sword.Buyers benefits include being able to negotiate terms, lower down payment, not having to qualify for a loan with a bank (if you have issues preventing approval).  

@Carolaine S.I would definitely consider selling the coop and look for a multifamily in a decent part of the Bronx or lower Westchester that would work for an FHA loan.

I'm no "pro" as well but I've listened to a lot of buyers in your situation end up in Option #4: Walk away for now and in time they may come back and accept your offer or in some cases accept an even lower offer. 

@John D.Depends on the interest rate you're paying, obviously the lower the interest rate the higher your return would be.

Recapture is the lower of the gain realized from the sale of property, or the depreciation deductions  taken on the business property .

Therefor you can find great cash-flow for less capital and lower competition from owner-occupants/flippers.Lesson to be learned is getting feet on the ground in those neighborhoods to understand the differences in product type and highest/best use.

This will hurt the lower income people that the rules was probably intended to protect.  

Yes, there are pockets of the city that support $1,250/month for a luxury 1BR, but one block over or across the street a lower-end 1 BR might be only $450/month, not $800.

I did quite a bit of research when I heard about the HELOC to pay off you mortgage and then using that account as your main account to funnel all your income and expenses in/out of etc etc.....the principle is that you will have on average a lower balance that your are paying interest on each month etc.....and read a lot about comparing that method vs just applying extra principle to your mortgage.

They may do it with just a lower LTV 60-70%.If they wont give you the HELOC I dont see why they wouldnt just let you open up a secured line of credit with the duplex being the collateral