You are asking me whether you ought to "bluff" your lender. I can't say whether the lender would call your bluff. In essence, you are hoping the lender will do all that is possible to keep you paying your mortgage.
Before you miss your first payment, you need to know whether the lender offers loan modifications, or interest rate and principal reductions. Some lenders, especially smaller banks or private lenders, will not discuss these options at all, regardless of whether or not you are delinquent or current on the mortgage. You could be bluffing with a company that will certainly call your bluff.
Once you verify whether your lender offers these options, I know that many people agree with your strategy. And I know that some borrowers do receive loan modifications after missing a few payments. A few of my clients have successfully received changes to loan terms. Unfortunately, those cases are the exception. Most of my clients who tried this strategy had it backfire and result in foreclosure. Of course, as a bankruptcy attorney, I would mainly see the negative results, but I do know that the vast majority of modification requests are unsuccessful.
In the past few years, clients have told me that the lender requires the loan to be delinquent before accepting an application. While lenders would likely deny this, I have heard this statement too many times from my clients to believe the lenders.
Let's assume you do take this route and stop paying the mortgage. You should save the mortgage payment, plus a late fee, and place that into a separate bank account. That way, you will have the funds available to bring the mortgage current in the event the lender calls your bluff.
Sorry I could not give a more definitive answer. It appears that you already reached out to the lender with no success, so your current strategy may be all that remains.
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