Sorry to hear that. I've heard similar happen to many people; how a bank can advice someone to fall behind on their payments is incredible to me. Bank of America wasn't the only one. And if you are able to make your payments, you don't qualify for a loan mod anyway, or any of the government programs.
You may already know this, but just in case. The reason why you may have been turned down for a reverse mortgage wasn't because you weren't qualified (assuming you are over 62) but because FHA currently has a lending limit of $625,500. It doesn't matter what your income is or your credit score is. Since there are currently no private jumbo loans available for reverse mortgages for high-value homes like yours, the only reverse mortgage program available is the FHA HECM. Unfortunately, because of the lending cap, any dollar over $625,500 that your home is appraised at is not given credit. How much you qualify for in a reverse mortgage depends upon the age of the youngest borrower (the older you are the more money you get), but only up to that cap. So while your home has a lot of equity, FHA only "values" it at $625,500.
That is why sometimes a younger spouse is removed from title when there is a large age gap between spouses. By using the age of the older spouse, they are eligible for more money. Not something recommended, but it is an option depending on your particular situation, if keeping the house is what you both want to do. Definitely something you want to discuss with a lawyer to protect the younger spouse's interest.
But you can still do a reverse mortgage, if you bring money to the table at closing. I don't know how much money you are short. Hopefully you were looking at the fixed rate product, which offers more money than the adjustable program, and can be found for as low as 4%. Some folks have other resources that they can sell or can access to bring money to the table, e.g. sell investment property, a car, stocks, life insurance, gifts from family or friends, etc. I don't know if this applies to you or if you are aware of it. The lender will want to document your source of funds to make sure it qualifies. Once you do the reverse mortgage, then that monthly $3900 stays in your pocket and no one can kick you out for non-payment of your mortgage. You will still have to pay your homeowner's insurance and property taxes. Just mentioning it in case you weren't aware. Good luck!
I specialize in reverse mortgages (CA)