The problem was that the straps kept coming loose on the trip to BI. I had placed an additional strap across the bikes for extra security, so they didn't fall off or anything, but at one point on route 80 the rack came loose enough that the bikes started flopping around.
When we got to our timeshare, I didn't notice any problems when I took the bikes off the rack. But the next day we discovered that the rim of my back tire was incredibly warped. The bike was just barely ridable because the wheel wobbled horribly. I thought I was in for a big expense of replacing the rim and perhaps several days without my bike.
Discouraged but resolute, I began looking for a repair shop. I was directed to a little shack at the Old Harbor ferry and found a cheerful young Greek man named Nikko who asked how he could help me. I showed him the wheel and asked if he could replace it. He looked at it and said, "Let's see if I can fix it first." He removed the back wheel and mounted it on his work bench in a way that he could spin it to see how much it wobbled to each side. Then he skillfully began tightening and loosening the struts while occasionally spinning the tire to check how much it veered to one side or the other. He spent a good 20 minutes doing this, working away like an expert piano tuner. I could see the tire begin to spin straighter and straighter until it no longer hit the guides on either side of the tire. When Nikko finished he put the tire back on and I tried the bike it rode well enough.
Nikko told me that he could have replaced the rim, but only with an old, used rim and at much greater cost. I told him the repair was fine and would get me through the week. And here's the kicker: the bill was only $5.00. Here I was on an island, at the mercy of people who could charge whatever they wanted, and Nikko said, "I can only charge $5.00 because the repair isn't perfect." Maybe the repair wasn't perfect, but Nikko was. You just don't meet people like him very often.