The best advice I've ever heard about coping with a "Due on Sale" Clause is this:
"Do not try to hide what you want to do. Ask the Lender before you move the asset into an entity."
IMHO, this is clearly a situation where it is far better to ask for permission than to ask for forgiveness.
If I am concerned about potentially triggering a DoS Clause, I will write a letter to the Lender, explaining what I want to do and why, as well as ask them if they will allow it in this one instance and waive the DoS Clause. The letter will be sent Certified, Return Receipt requested, and the Return Receipt will go into the file that holds the property's paperwork, along with a copy of the letter. If the Lender ignores you, that Return Receipt will become an essential piece of evidence. If the Lender agrees, you have no problem in transferring the property; if they state that they will invoke the DoS Clause if the property is transferred, you know where they stand on the matter (so don't try to work around it).
There is a time limit on their ability to react to you transferring a property into an entity in violation of the DoS Clause. It may actually be a "Statute of Limitations" issue. If you hide the transfer, the time limit doesn't START until the Lender discovers the DoS Clause was violated (even if it's many years later); if you ask the Lender ahead of time, the time limit starts when they receive your letter asking for permission (which means the clock will run out sooner, rather than later). Also, if the Lender allows the transfer, then later claims they will invoke the DoS Clause, you have recourse (in the extreme, you could ask for a court to issue an injunction, etc.). Start by showing them the letter giving you permission.
I'm not qualified to answer to the insurance aspect of this matter - consult with a pro!
I've had some experience in transferring real estate into and out of estate planning trusts. I'm a little surprised that the attorney posting above didn't state that transfers into and out of Living Trusts are exempt from DoS Clauses by federal law. The difference may be whether the trust is "Revocable" or "Irrevocable". I've successfully used Quitclaim Deeds to effect the transfers. They included notices that the transfers were exempt from transfer tax and stated why they were exempted (check with your local Registrar or your local Attorney on this issue).
This doesn't mean that you can use this approach to 'dodge' the DoS Clause.
One important thing I've learned is that you really should read and contemplate the meaning of the DoS Clause in your loan documents. I've seen DoS Clauses that are triggered by "...sale..." and others that are triggered by "...any transfer of beneficial ownership..." (regardless of whether it's a sale, foreclosure, gift to relative, etc.). The more restrictive the DoS Clause is, the more important it is to ask for permission!