I honestly have never heard of Eagle Lake, but I know that the hatchery has top quality fish. I guess it would be pretty convenient for you to pick up the fish there lol.
Potential legal/eco problems here. Definately check your local regulations. How "secret" is the pond and who owns the land? If this isnt your property you may not want to get caught. I say its a slippery slope from someone introducing goldfish and bass to snakeheads and disaster.
My opinion is just enjoy the pond for what it is and watch how nature develops it.
Just my opinion though. Very cool that you have something like this nearby though. I live in the desert so dont have the opportunity.