OK, I stand corrected. I just needed to be smarter than the Mediawiki.
I've always noticed in hidden text boxes that we seem to have an extra line break inserted after the first and before the last lines of any text inside the template. And that, as it turns out, is exactly what was screwing this up. Now that I know how to view the rendered HTML that gets spit out ("?action=render"), I can see that I'm not imagining the extra line breaks because the template actually does create a separate paragraph for the first and last lines of any text inside the hidden template.
In case 7, I just inserted a random character to see if I could force Mediawiki to parse the entire table inside the same paragraph section. It turns out, I could, and that was all I needed to hide the table intact.
In case 8, I replaced the period with a nbsp tag (just hitting the space bar is interpreted as "nothing" by the parser, so that works differently.) Viola. I appear to have found a solution.
See case 9 for the final outcome.
(And I'd appreciate it if anyone knows what the "correct" way to modify that font size in the hidden header if they'd share with me what that is.)