I eventually got it to work by creating a folder containing the Messages app and another app. I was then able to drag the Voicemail app into the folder and delete the third "crutch" app. It was Voicemail that was the culprit apparently. (BTW, why do I even need that app on Sprint? I never used to. Can't I continue to use the "1" shortcut?)
One comment said to use the shortcut, not the app. As far as I can tell from the feedback I get when installing apps, all the icons shown on the home screens are shortcuts. I'm not sure how I would tell the difference.
Thanks for the responses. I have a skosh more space on my main home screen now.