If you're going to be using it for more than a minute at that power level, you will need water cooling.
I think the Miniductor doesn't (or claims not to), because it has that fiberglass weave stuff over the coils, and is only intended for intermittent use anyway. They'll get *very* hot under there.
A "ZVS" or "Royer" driver puts +V on the coil, which is inconvenient for grounding against most power supplies. You can, of course, simply use a positive ground system for that circuit.
My induction heater design, and most industrially, are made with isolated or grounded coils. Water cooling is trivial; water doesn't care about AC (specifically, for frequencies above the ionic drift rate in water -- probably something like 20Hz for flowing water).
Tim