Just to give you an idea about paddlefish keeping, I've got three in a 225,000 gallon. They're still small. The tank you have planned sounds great, just not for any of the fish you listed (arapaima, paddles or tiger muskies).
If you were to do the legal paper work and then build the tank, I would suggest something round, and in excess of 30'. Depth isn't too important, even at 6-7 feet deep, it will be ok for life. Get the tank up and running for about six months, then get the fish. Also keep in mind you'll be feeding three times daily (if not more). You'll really plug up filters fast with the feeds since (like was said) they are filter feeders for the most part, and require a LOT of food to be broadcast into the water.