Oh, distance always matters. The parabolic shape is, as I recall, the most perfect one for focusing light from a distant object onto a point, and the parabolic dish has a natural focal point. By making the surface out of many small adaptive mirrors, you can move some away from that focal point without losing a whole lot of the energy, but it isn't like you can aim at something a mile off and expect to burn a hole through it - the farther you are from the natural focal point of the parabola, the less energy you'll be able to deliver.
well, my theory was, if you had the mirrors that could pivot, they'd always be angled to bounce the sun onto the target.
This might be akin (though not technically correct) to having the mirrors on a dish that could flex, becoming flatter or deeper (thus changing the focal point.
the fixed mirrors on a fixed parabola is what gives it a fixed range, which is why distance matters for it.
For a rig with flexi-mounted mirrors, it could change the focal point, thus distance doesn't matter (to the extent they can all be kept aligned)
I got a rough idea on how to keep 1 row or mirrors aligned on a target. But making a larger array of rows with this feature and keeping it portable is trickier.
one random idea:
get a sturdy ring and stretch cloth over it. Then mount the mirrors on that.
Then pull the center of the cloth back, which would cause a curve to form in the material.
I think one of the mythbusters deathray episodes had somebody with something similar. Though there it was like mylar, stretched over a drum, and vacuum presure or something caused it to curve inward, forming an adjustable disk.
I also wonder about the burning of the shed that housed the death ray. Seems a little coincidental that fire making device burns up in a fire. I suspect the kid did something stupid.