I have asked my host (Firehost) about it, but they weren't able to give me much of an explanation. At the time when I asked them about it, my assumption was that some changes we'd just made to the server were causing the issues. Ultimately, we did a full server rollback, in part because of this error. Later, I discovered that the error seems to occur only on my sites hosted by Firehost, and only on those running a version past 1.0.4. I'm currently hosting sites on Bluehost and on GoDaddy, and neither of those seem affected.
I've temporarily fixed the issue on my Firehost sites by using the earlier version (1.0.4) of Types; however, I'm a stickler about keeping everything up to the most current version if at all possible.
In wp-config, I added the following code (starting with enabling WordPress debugging):
define('WP_DEBUG', true);
define('WPV_LOGGING_STATUS', 'debug');
ini_set('log_errors',TRUE);
ini_set('error_reporting', E_ALL);
ini_set('error_log', dirname(__FILE__) . '/error_log.txt');
However, after running through the process again (and seeing the blank screen), I'm not seeing anything either in the console or in any of my folders (an error_log.txt file doesn't seem to be generated).
My apologies; I know that's not helpful. Thanks again for your help, Caridad!
Oh -- to add to what my host had said, from our exchange, they gave me the following errors (however, I don't know precisely where these came from, since I assume they didn't go through the same process of attempting to create a post type). Here's what they told me:
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As to the white screen in the taxonomies page, we briefly enabled debug mode in wordpress to ensure that we had proper error output. Below is the output wordpress normally suppresses when posting to that page:
Notice: Undefined property: RTE::$debug in /home/a553/public_html/wp-content/plugins/rich-tax-description-editor/i8/class.i8Core.php on line 17
Notice: Undefined property: RTE::$options in /home/a553/public_html/wp-content/plugins/rich-tax-description-editor/i8/class.i8Core.php on line 542
Notice: Undefined offset: 2 in /home/a553/public_html/wp-content/plugins/rich-tax-description-editor/i8/class.i8Core.php on line 167
Notice: Undefined offset: 1 in /home/a553/public_html/wp-content/plugins/rich-tax-description-editor/i8/class.i8Core.php on line 167
Notice: Undefined offset: 2 in /home/a553/public_html/wp-content/plugins/rich-tax-description-editor/i8/class.i8Core.php on line 167
Notice: Undefined index: action in /home/a553/public_html/wp-content/plugins/rich-tax-description-editor/i8/class.Plugino.php on line 74
Notice: Undefined index: HTTPS in /home/a553/public_html/wp-content/plugins/simple-301-redirects/wp-simple-301-redirects.php on line 143
Notice: Undefined variable: control_ops in /home/a553/public_html/wp-content/plugins/all-in-one-slideshow/all-in-one-slideshow.php on line 46
Notice: Undefined property: RTE::$pages in /home/a553/public_html/wp-content/plugins/rich-tax-description-editor/i8/class.i8Core.php on line 282
Notice: has_cap was called with an argument that is deprecated since version 2.0! Usage of user levels by plugins and themes is deprecated. Use roles and capabilities instead. in /home/a553/public_html/wp-includes/functions.php on line 2722
None of these are deemed critical by apache or php and thus the page returns a 200 and no errors end up in the logs. Hopefully they will be helpful in diagnosing the root cause of the issue. From what I can see, this is not an issue with any configurations on the servers themselves.