There's always graters for those who are bothered by the fact they're not tighter fit. I would be more bothered if the puck would not fit the dish. Lather and let lather, friend.

As you noticed, the puck will stick. Also with constant use without incessant drying, the puck will expand to fill out the dish nicely.

Haven't tried, but IIRC milled tallows won't melt well.