The company's insurers will also lay down minimum experience levels, for all flight-deck crew.
Not strictly true. Underwriters accept that companies operating under an AOC will have Operations manuals approved by the legislating authority that will contain minimum hours requirements for various positions that are considered sufficient, so allow them to self regulate. When it comes to smaller companies, what is known as a 'Pilot Warranty' may be included in the insurance cover that stipulates minimum hours for pilots in that company, i.e. for a Twin Otter it could be something like, "1,500 hours total time with 500 on type", (that is just an example), that company could then approach underwriters and say, "We have a pilot with 5000 hours total, all relevant, will you accept 250 on type?" , almost certainly, from my experience, it would be a "Yes' without additional premium. Another example would be a company buying a high value, one off, corporate aircraft, the underwriters would certainly want to know the pilots experience before covering it.
All the above does not exclude the possibility of an AOC company with a bad accident/claims record having pilot warranties introduced, if thought necessary.