OF course deductible and and amount covered will be mostly a financial decision. I don't know anything about OP coverage. I suggested he ask since he doesn't have $6K kicking around.That is a assumption the insurance company may pay out $6k USD. Maybe the insurance company only pays out less than the deductible, which means they paid out nothing. Yet the property has a reportable insurance claim. And the insured has a exposure to being rates raised or cancelled.
Something I was educated in by a insurance actuarial, it is not the amount of the claim the insurance company cares about, it is the amount of claims.
Filing a claim with an insurance company that results in zero payout by the insurance company, and filing a claim that the insurance company pays out $80k USD, are both viewed as placing a equal claim. Of course, a $80k USD payout by the insurance might get the insured dropped from coverage quicker than a $0 USd payout, but that is a separate subject.
This would be a single claim. But you never actually answered my question/concern.
For the record, personally I would just pay to have the ditch dug, etc.