Everything is okay (until the next problem).
First, to explain what happened from the start: My engine had been overheating and the flow of water out the exhaust seemed minimal. I started by opening up the raw water pump to check the impeller. Although it was okay, it's been well over a year since I changed it, so I put a new one on. I tried starting the engine, and at that point no water came out the exhaust at all. After much fumbling around, trying to figure out what I'd done wrong, I started taking hoses off. I figured something was blocked at some point in the line, so that's where I came up with my "stroke of genius":
I took the hand pump (the one that looks like a bicycle tire pump) and taped the end of the hose over the hose that leads from the engine water pump to the heat exchange and pumped some water through there. I think it was a couple of quarts. Then I tried it again, but still no water coming out the exhaust. Then I took off the hose that leads from the heat exchange through the vacuum break to the muffler. The elbow and nipple screwed into the heat exchange was almost entirely blocked with what looked like salt. I unscrewed that and cleaned it out. However, the nipple had come out of the elbow so I had to take it home to solder it back in. (It was only press fitted originally.) That night, I woke up in the middle of the night realizing what I'd done as far as pumping water through the hose. I haven't slept well the last two nights worrying about it.
Stu helped talk me through things. (Thanks so much, Stu!) He explained that the first place the water would go to would be the muffler, which he explained holds quite a bit more water than I had pumped into the hose. He also suggested that I open up the petcock on the bottom of the muffler to drain whatever water there was in there. (We figured that was where the water had gone.)
I did open up that petcock, but only about a tablespoon of water came out. Before starting the engine, and just to be extra safe (in case my memory was mistaken and I had not run the engine after pumping the water through), I took a wrench (a 12" crescent wrench worked) and turned over the engine a couple of times. I also checked the oil, which didn't show any signs of water in it. So at at that point, I was pretty confident that there was no water in the engine. When I cranked up the engine, water came out the exhaust in what looks like a good flow and the engine didn't overheat.
One mystery is what happened to that water I pumped through the hose. The only thing I can figure out is that maybe it stayed in the muffler and shot out immediately after the engine started the first time (the other day) and we didn't see it. Either that, or "good" gremlins. Another thing is that I would have thought that if the problem was purely the blockage of that nipple/elbow, that that would have occurred over time, meaning the flow of water would have been restricted slowly over time, meaning that the engine would have started running slightly hotter and slightly hotter over time. That didn't happen, so I'll have to keep an eye on things.
It's been quite a while since I've checked back onto this site and I'm so glad to see it's still going strong. Thanks to those who have kept it going and a million thanks to all those who offered suggestions. It's beautiful and windy here on the SF Bay, and I'm going to be thinking of you guys when I go out in the next few days!