I'm sort of like the opposite of this fish; I imagine my swimming looks to him like his walking would look to me. However, after the great advice everyone gave me the other day, I've been experimenting with swimming some more, and I feel like I'm getting closer to figuring it out. I think the turning point was the suggestion my M to watch the Total Immersion swimming videos on YouTube. After watching a bunch of those, I started to figure out what I was doing wrong, and was able to try to change my stroke up. I'm by no means good, but the day I swam after watching the videos, it was so much easier. I was able to swim twice as far that next day as I had been, once I streamlined my stroke and didn't have all this wasted effort and energy (it's still not very far, but much better than it was last week).
The bouy has been really interesting, too. Not using my legs at all has not only helped me concentrate on my upper body, but it helps my knee a lot; my knee hurts when it's bent (i.e. when sitting), so keeping it straight relieves the stress and gives me some release from the constant ache, which has been getting worse lately.
As I've been having fun trying to figure this out for myself, and only I have 3 weeks and change until surgery, I talked to my friend who said she'd give me some advice, and we're going to wait until after the surgery, so I can just play for the next few weeks by myself.
I've either tried or been thinking about much of what you all told me when I've been in the pool this week, and it's definitely helping this whole swimming thing make sense in my head, so thanks again for all the good feedback!