PNP-
that exact same thing happened in my boat 2 years ago, below poacher cove. The fish came up on my buddies rod, but like you, we stood around saying what-the-f#$*, as there's the spin-glow but the rod is still hitting the drink.
Luckily, our drift set-up had a much shorter leader than your diver-quickie. Our hook was also through the swivel, but we were able to boat the fish. The kicker is that the fish was 50 pounds. That's story number 1. Now to the best story of them all...
Last Year the same thing happened again, but this time in my fishing partners boat @ falling-in. The exact same thing happened as yours, being on a quick-fish, and hooked through a swivel. Because of the amount of line out below his rig, my friend wrapped the line around his jacket, the other guy cut and tied tied a blood knot to existing line, and they landed the fish. Here's the kicker of ALL kickers. The fish weighed an even 62 pounds.
The funny thing, they didn't seem that impressed by their teamwork and quick-thinking. When you fish the Kenai every year however, it's hard to get impressed anymore. More like depressed! Actually, there's A LOT of fish swimming around the kenai with knots and swivels dangling about. It's a fairly common occurance