Anytime I need to route a profile on the end of any boards, I just use a scrap piece of plywood about 8" square. Throw a handle on it (shaker peg?) and use it kind of like a miter gauge.
It's hard to describe, but for horizontal passes, I set the square on the table against the fence and the workpiece against the square corner created by this - so end of the board on the fence, back edge of the board on the square piece. Push with the hand on the square piece and use your free hand to keep the workpiece tight on the square piece. It's harder to describe than it is to do.
For vertical pieces, same thing, just on the fence. Square piece flat on the fence (vertically), workpiece against the leading edge of the square piece and the end on the table - just like you've been doing except the square piece gives you that all important no-wiggle support.
Another advantage this offers is that it will backup the wood on the exit of the cut so it can reduce tearout when the bit leaves the workpiece.
Maybe you can adapt something like this to a shaper? I'd offer a picture, but it's just a square hunk of plywood with a knob in the center.