Well, I went down to the work shop and took a long look at the bowl and did a little measuring as well and it turned out that there wasn't a lot of wood left between the ends of the screw holes and the bottom of the inside of the bowl. So I turned the bottom more convex a couple of millimeters. This deepened the bowl, improved the appearance, and added a little more volume. Here's what it looked like immediately afterwards:
And I decided to stop there. It's not worth the risk of cutting into the screws and ruining the bowl. I sanded and oiled it and here it is at present:
I'm going to oil over the next several days and give it a beeswax finish at the end and polish it. I'll post more photos when it's done.