I finally got to use my hand plane yesterday. I bought it almost a year ago, but never really used it for anything until now. I used it to even out some high spots in the body since sandpaper wasn't doing it quickly enough. I did have some tearout along the edges, and in the surface, but luckily, I haven't cut out the final shap yet, so the edge tearout will be cut off. As for the surface tearout, it will either be cut out when I chamber the body or covered by the spruce top that's going on this.
And then, with much skepticism, I used my router, equipped with the 1 1/2" (the other day, I said it was 2" -- I was wrong) flush-cut bit to trim the poplar laminates for gluing. I had a few tearouts that meant trimming the poplar down a bit more than I wanted to, but the end result was two halves of a body, ready to be joined by a center strip of rosewood.
Speaking of rosewood, I thought the 1/4" piece of scrap would be thick enough, but it's not. The total body width of my Serenade design is ~13 3/4", but right now, with the current piece of rosewood, it's only ~13 1/4". There's no technical reason why it wouldn't work, as is, but a design is a design, and this one calls for a body width of 13 3/4".

So Larry, if you're reading this, expect an order for 1" x 1 1/2" x 18" rosewood, as well as other woods for a body and neck blank, and maybe a top (myrtle?).
In related news, I've decided that my standard body width will be 1 1/2". Before I trimmed the body down, I realized that 1 3/4" was just too thick for me. I also realized that my other basses are 1 1/2", so that's just what I'm used to.
EDIT: Added a photo.