I can't speak directly to the K6-2, but when I lapped my P3 the technique I used was to put my thumb and index fingers on the four corners of the chip, in such a way as to support the chip on the paper as level as possible. I suppose you could even have someone check it in two planes with a bubble level. A bit anal, but hey - this is serious stuff.
By maintaining a constant degree of light contact with your fingertips and the paper, you can keep it pretty level by feel. Increase pressure ever so gently as it laps. And yes, you do lap your fingertips in the process, but we're not talking 80-grit paper here anyway.
Pressure in the center, especially if you sand in a circular pattern, is more likely to round off your edges as you describe. I used a figure-8 pattern.
Folks who have more experience with the larger surface area of your processor, feel free to weigh in, but this way worked OK for me.