It appears you are at an impasse with your insurance company over the reason that the engine no longer operates on your Honda. I would have another mechanic check over the vehicle to see if he can do a diagnosis without pulling the engine. If the engine must be pulled I would definitely get a few other quotes because the quote you received seems very high and possibly the price of a new engine and not just the removing of the used one.

If you cannot afford this work on your own to show proof of the origin of the engine problems to your insurance company you might want to seek legal advice on what actions you can take.