Thanks, John. Didn't see your post till just now, after I sanded it with 120 grit (the disc that came with the sander). Slow going with that grain, but that's good, since it made it more idiot-proof. I'll get some coarser grit, as you suggest. I did (as all can see) put some pretty nasty gouges in the paddle with the plane--but they'll come out, I'm sure.

It's a really fun process.

I'm with Brian on this.
I'd recommend hand sanding starting with coarse (40/60 grit) paper and a hard sanding block that uses the full length of the sandpaper sheet.
It will go pretty fast.
You really don't want to have any 'hollows', and with a soft wood and a sander it's easy to get them when trying to make things 'smooth'.