Falcon is a broker not an insurance company and insurance carriers only want one broker to quote to, you can't go to multiple brokers and get quotes, so if you go to Falcon you cut the broker you now have out of the deal ,and Falcon gets the commission off the back of the first broker
There are only so many insurance carriers out there and the list is getting shorter, stick with the broker you have and ask him to negotiate a better deal if he can.
Self insuring and putting the money away as you mention, dumb idea, unless you are daddy warbucks and have too much money, you won't save the money and you can't put enough away to pay out a large loss, what if the plane is totaled in a year? did you set aside enough money to pay for the plane?
Nope you did not, how about you crash and kill some one or burn down a factory, but you survive or you if you die, some lawyer is going to sue and put your family out of a home, because you dropped your coverage to save a few bucks, you need to understand risk and not complain about premiums going up, ask yourself this, Can I afford to lose the value of my airplane or do I want to lose it,? and can I afford to take a huge financial hit if I get sued.
I don't know what your BO is worth but land gear up and the carrier will total it and pay you the hull value, BO's do not exactly have the best nose gear, so the carrier looks at risk vs reward example only: premium $2,500 say hull value $150,000 , total loss, who wins ?
Insurance is for : Do I want to take the risk on my own, or can I afford to do it?. Think worse case scenario of what you can afford to lose
Take a higher deductible if that saves premium,