I ran into the same problem at first. My plan of attack now is to prepare the package and fill up the test water prior to even firing up the checker. For the packet, I hold it along the sides where the cut lines are with two fingers on each side, then wiggle the reagent down into the section without the cut line. After wiggling it, I hold the packet with one hand and flick it with the other to get everything away from the cut lines. Since there are two sides with cut lines, I repeat this process for both. Once done, I cut along the cut lines. After the cut, I try to determine which of the remaining sides has most of the reagent settled against it. After making an educated guess on this, I turn the packet so this side is on the bottom, fold it there along the seam, and try to gently maneuver all remaining reagent to to the bottom.
Once the initial stage of the test is complete and it's time to add reagent, I hold the glass container on my knee (while sitting on the floor) and use my other hand to open the reagent packet into a "V", then tap it lightly against the glass rim. Since it's open in "V" shape, the opening is wider as it goes up, so that gives you a surface to hit against the glass and force everything out, while aiming it directly into the container.
