So found a way to add rounded corners and played around with them until they looked close to right. There are still a few places where the spacing is less than ideal, but I do not know CSS and adjustments were mostly trial and lots of error. I kept the black text on a white background, but then I framed everything in BYU-blue. I made a nice (and correctly sized) banner and drastically limited my clutter with widgets. I still hand-changed the template to have the sidebars on the right like I wanted them. You may not believe it, but I did exercise much restraint. In the end I had something that looked decent.
Apparently I did this two months too soon. On March 11, Blogger announced the Template Designer in Blogger draft. You can read about it in the Blogger in Draft blog or the Blogger Buzz blog. Basically, all the blind bumbling I did in CSS can be eliminated by using one of these templates.
My favorite right now is the Picture Window by Josh Peterson, although there are several templates available that look really sharp. I thought about and even tried moving my blog over to one of these templates, but there were some things that didn't look like I wanted and I liked being the master of my own template. If you are starting from scratch, I would completely recommend using one of the new templates.