I still don’t have a scrub plane, so milling this piece of european beech for my future mallet was as time-consuming as you’d expect:

To minimize the pain, I just flattened one side and then scribed the other side for about the maximum thickness so that I wouldn’t have to take off too much stock. I don’t even know how thick it is, just that it’s pretty much uniform. We’ll see why this doesn’t matter in later stages.
I used the jack plane quite a lot more for this one. Working straight across the board and in diagonals took out the cup fairly quickly. The fore plane rounded out the first face, and this side turned out very, very flat.
There was more work to do on the other side because there was still a significant amount of stock to remove, so naturally, it took a long time. In addition, I decided to goof around with one of my smoothing planes again, trying again to improve its tuning. This went fairly well. I managed to tighten the throat a bit and straighten out the frog.
Moreover, I figured out a trick on how to straighten the frog: if the sides are square, you can use a double square. Put the stock on the frog bed (where it meets the blade), and extend the rule out over the side. If the frog is square, the rule can sit flush with the side of the plane, because those two surfaces are, in theory, supposed to be orthogonal. I suppose that a photo would be handy here, but I’m too lazy right now to show it.
The downside of all of this messing around with the smoothing plane is that in my excitement, I took off a little extra from one of the edges, making the second side “not quite flat.” In the grand scheme of this project, it does not matter. In fact, it might be a good thing.
The only thing that does matter is that the next thing I mill down had better be for the body of a scrub plane.