Kevin
Having worked in the insurance industry for 18 years and yes, I am an adjuster that has handled boat claims, I would agree your insurance company's request is not the norm. It may, however, be what THEY require and of course, they control THEIR money so you may have to play by THEIR rules (hey, I am a consumer first, adjuster second so I understand the frustration with rules).
Usually, an insurance company requests a detailed estimate be provided so they can review the repairs are consistent with the damages being claimed (and that the stated cause is consistent with those damages). That is usually enough to be the "Statement of Loss" or the "Proof of Loss".
Once reviewed, an actual cash value payment is made (if items are being replaced, they are paid at a depreciated value until the insurance company receives documentation that the parts were actually replaced, at which time, the insurance company would send a second payment, more-or-less refunding the depreciation).
If you are just getting the work completed straight away, you should be able to submit the bill (assuming the insurance company approves it) and get paid the full amount, minus your deductible. I am a bit surprised at the notarization requirement.
I have had my own boat claim and it was simple: the adjuster met me at where I stored my boat, looked at the damage (bent prop shaft, bent propeller - guess what I did!) and paid me based upon my estimate. Very simple.
One thing though, you really do not want the insurance company to pay your contractor or repair person directly...remember, it is your property, your claim and your benefits and you should maintain an interest and control. Not that a contractor or repair person would do something shifty
; however, if they did embellish or fib, you would ultimately be responsible...keep an eye on your interests.
Also, it is great to save money on insurance; however, look beyond the cheap companies to the ones that do provide adjuster inspections and/or have local or reachable offices. Remember, you do not pay insurance to save money, you pay insurance to receive good benefits and good service when you make that claim.
Good luck
Louise