For planing panels I plane against a two inch wide bench stop, which is mortised into the bench. The stop can be adjusted to protrude a little less than the thickness of the panel. There is no need for a holding device at the other end of the panel.
The largest 1/4 inch panel I recall planing in this manner was 14 X 21. In traditional work, however, we would rarely make a large panel this thin. Eighteenth century frame and panel is typically 7/8 or so for the framing, with a 5/16 groove for the panel. And a flat panel is typically slightly chamfered on the back side (to fit into the groove), so that the thickness is closer to 7/16 or 1/2.
For very thin stuff, less than 1/8, we sometimes clamp the piece and plane away from the clamp. This technique is inappropriate for a panel because you can't take full planing strokes in one direction so visual quality is compromised.