Per the comment on the original question and work with hosting technical support, the problem was indeed the child theme. Both the comment and tech support gave me a possibility to pursue, but not a conclusive answer. So, here is how I pursued it.
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The parent theme was Twenty Sixteen. The child theme only had the very basic code required in functions.php and about 50 lines of CSS changes.
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To test whether the problem was indeed the theme, I installed Twenty Seventeen and activated it. It activated fine, and I was able to edit a post without the white screen of death.
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Then I went through the same procedure to create and activate a child theme using Twenty Seventeen as the I had for Twenty Sixteen. I was able to edit a post without the white screen of death.
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I deleted both Twenty Sixteen and the Twenty Sixteen child theme.
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I re-installed Twenty Sixteen and copied the child theme from Twenty Seventeen, changing the folder name and the template. At this point, the child theme was using all the resources of the parent theme. I was able to post and edit without the white screen of death.
This brings up the further question of precisely what caused the child theme to break the posting functionality, but at least we can move forward with the site construction.