I suspect the only solution is to build a shooting board which is a piece of ply or MDF (or wood) with a second piece, narrower by 10cm or-so, attached to it.
Mount a dead straight piece of Oak or some other hard wood perpendicular to the two pieces of ply to for a fence. Also fit a batton underneath the opposite end of the assembly to form a hook that will push against the front of your bench when in use.
Clamp or hold the workpiece to the fence with the end to be planed level with the edge of the upper plywood. Run side of your plane along the lower board with the blade pointing towards the workpiece (plane lying on it's side). The base of the plane will run along the upper piece of ply to guide it towards the fence and workpiece and will plane the end absolutely square without breakout.
Try clamping an offcut of wood to the far side of the piece. Make sure it is level with the workpiece. As you plane down the piece, the off-cut will chip out, not the workpiece!
Or you could build a "shooting board" which will allow you to cut end grain without it chipping out. i'm sure someone here has a plan for you.