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So I used the Homax peel & stick tub & wall caulk strip. Even though I know you're supposed to remove the old caulk first, since it was so narrow I left it on and put this right over the top of it. I also used some clear silicone to touch up a few other spots (around the handles and such).
First I cleaned all along the tub and wall real good. I used a bathroom cleaner, water, then alcohol. I let it dry for several hours, then put the stuff in place. It was pretty easy to do. I just hope it works now, otherwise I'm going to have to start over from scratch. We'll see.