Another Tip You'll Like Too
Here's another one you haven't seen either. In an emergency, for thicknessing just one thin stick, I set this up in a Black and Decker Workmate years ago and it worked. I thought you'd like it. And the great advantage is that it's almost an instant setup. Additionally, it offers an infinately adjustable angle-of-presentation so no angle finding, no sliding bevels and protractors needed. Just adjust according to 'feeling' for the cutting edge when you pull your wood through. Depth adjustment in this case comes from adjusting the clamp in the vise.
There is not much to tell you beyond what you see in the pictures so I will just park it here and leave you to it.

Use whatever support platform you have to hand. The plywood platten worked because the bench top was ragged. The two-by-two was just a simple way to clamp a support bed to the benchtop. What you cannot see is a layer of silicone shelf liner between either one of the clamp heads and the card scraper to stop slippage and it does not slip with this in place.

Move tighter up nearer to the side of the clamp where there will be no flex for the final thickness. Just keep passing your stock through the flexible side until it stops removing shavings and then move in to the other side. You can also press the card scraper to take off heavier shavings.
Additionally, as an afterthought really, you can move your scraper across from side to side as you lose the premium cutting edge. With the four cutting corners and working on 12mm wide or less stock that's a lot of 'planing'––many a hundred metres at least!
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