@Javier Gil THIS IS NOT LEGAL ADVICE, but I'm going to tell you what's really up with the due on sale clause to save you from wasting tons of money.
I haven't seen banks foreclose based upon a due on sale clause on performing notes, nor have I or my colleagues ever seen a foreclosure prosecuted under those circumstances.
This is not legal advice and you are not my client, but I believe the risk is very low if you deed the property into the LLC ($200 likely total cost) and ignore the bank; if they begin foreclosure, cure the breach of contract by deeding it back to you (which I would be shocked if it came to that) and then whole process should halt at that moment. The cost/benefit/risk seems more attractive than the costs of refinancing (higher rates, closing costs, etc.)
Now for some speculation...
We believe that it has to do with the fact that it is bad business for the banks, and we believe that the bank attorneys have to justify their budget so they add a huge line item around "notices" to make it look like they are doing a bunch of work even though it is basically worthless.
The fact is that when a bank forecloses it is bad for business -- they will likely lose money on the foreclosure and REO sale and their rating goes down for issuing "bad" notes. A bank literally fails at their job if they issue a bad note because banks are in the business of loaning money and collecting P/I payments. If you work in corporate America and are the boss overseeing this, do you want to be the one that loses your company money and also hurts it reputation?