I work in the insurance business on behalf of policyholders. The insurance market will not go under from these two events. Far from it. They will use the losses from Irma and Maria as an excuse to raise rates and eventually they will profit from the storms. As far as paying claims the total loss vessels will be paid at hull value per the contract less the deductible. In some cases the deductible is 10% so be prepared to come out of pocket that amount.
On damaged vessels the surveyors hired by the insurers will come with an estimate of damages. They will attempt to settle the claim based on that estimate regardless of market conditions or the availability of qualified repair yards in the Leewards. To get a damaged BVI yacht repaired it will need to be transported down island or to the US. Or you can wait 2-3 years for a slot to open in the VIs.
If you have a damaged boat in the VI push to have it totaled then negotiate to buy back the salvage. The boat is likely worth more to you than the insurer so there are opportunities to be had that benefit both sides.
Insurance is a for profit business. Lloyds members have not gotten rich over the past 400 years by paying claims quickly or by settling at fair numbers.
Good Luck.