If you let the frogbit alone, the roots will eventually grow all the way to the substrate.
I am so sorry, Matt. I have yet to have any casualties like that, your goldies must be particularly voracious (most goldies are.) I would put it in a jar in the window, not in direct sunlight but were it will get bright light for most of the day. You can add a small piece of shrimp pellet or some either meaty food, just a tiny amount, every so often and that will "feed" it. Just make sure to not let the water get too nasty, and still rotate and clean it every so often.
I have one in a jar in my kitchen and it pearls every 3-4 days, definitely neat.
Kristina