It turns out that the WeCheer carving machine does a fine job. The handpiece is fairly comfortable, and the motor unit is quiet. When the chisel is engaged, it is fairly noisy, so hearing protectors are in order. Working with the grain, the resulting cut is clean. Cross-grain tends to be a bit messier. Despite those positives, I went back to the finger plane.
The power carver has one big advantage... comfort. In every other way, the finger plane has the advantage. There's more control, the cuts are more consistent and cleaner cross-grain. And it's much faster. I can take a dozen cuts with the finger plane in the time that the power carver takes one cut. Then of course there's the noise level. The power carver sounds like a machine. The finger plane sounds like a plane swishing though wood. I find that a far more pleasant sound.
Two hours of work resulted in almost half of the back plate having a rough shape. I think another 5 hours or so should get it close to the final profile.