For lump in the kettle, I use a second grate on top of the old grate. I turn the old grate upside down so that it's support rails face up, and place the other grate on top with the rails running crosswise. It locks itself into place.
It helps a lot in retaining the smaller pieces, as the grates form a grid. Using lump takes a little getting used to, but it's not harder to use than charcoal, just different.
Haven't tried Kingsford lump, but I don't think it's reviews were very good on Naked Whiz if I remember right.
I've been using Royal Oak, and Wicked Good without any major problems.