You don’t need an industrial-sized thickness planer to flatten large slabs of wood. It’s actually possible to do it with your router and about $20 worth of material.
Using a heavy-duty router equipped with a 1-inch-diameter top-bearing flush cutting bit, a shop-built sled, and two rails, the Samurai Carpenter planes the top of a large slab of wood. In the video below, he talks through his process, which includes how to level and shim the rails and slab (note, he actually splits the difference when there’s a big discrepancy in thickness), what size to make the sled box, and his choice of material for the rails. The box is built so as to avoid sagging, and he’s careful to make passes in small increments (about ¼ inch at a time) to maintain control over the cut. It’s a simple and straightforward solution for planing, especially for large, wide surfaces.