Keep the filling from wetting the rye

Drain and squeeze the sauerkraut before building the sandwiches. The dressing already supplies moisture, so wet cabbage can soften the bread before the cheese melts. Divide the filling into three piles beside the bread rather than filling the first sandwich generously and leaving the last one short. Keep the buttered surfaces on the outside.

Have a plate ready before the skillet heats. Once the first side is crisp, turn with a wide spatula that supports the sandwich instead of gripping its middle with tongs.

Give the cheese time to melt

Medium-low heat lets the filling warm while the bread colors. If the rye is getting dark before the cheese softens, reduce the heat rather than pressing harder. Pressing can squeeze dressing into the pan and make turning messier. Cook in separate rounds when the sandwiches would touch or prevent the spatula from sliding underneath.

Keep the small pause between batches brief and serve from the first finished round if needed. A crisp sandwich is most enjoyable soon after cooking; making all three fit a cramped skillet is not worth losing control of their surfaces.