Lacking an answer, I came up with a way to fix this myself. Posting this in case this helps anyone in the future.
Firstly, let's not do this infobox thing with tables; it isn't the most appropriate way to do structural elements anyway... and your Minerva and Mobile style sheets will mess up your tables. Let's do this with DIVs. Secondly, this requires defining some DIV classes that will be styled differently in Common.css than from Mobile.css so that you can have a full-width infobox in mobile in which the contents remain centered. Thirdly, it looks like the way MediaWiki does thumbnails doesn't like to play well inside "infobox" divs (or tables) like this when viewed on wider-screened mobile devices, such as tablets and phones in landscape (it'll stop center aligning and instead hang left of center after a certain width), so let's go ahead and wrap that image wikitext with yet another DIV with a class that's styled in mobile to make it actually stay centered irrespective of the containing infobox's width.
Markup for a right-aligned infobox containing a thumbnail image, a centered heading above the thumbnail, and a div below. Keep in mind you can clean up your page by relegating most of this markup to a template and calling that template in your article rather than having an article cluttered with markup:playing home to left-aligned content:
<div class="infoboxright" style="background-color: #EEEEEE; text-align: center;">
'''Heading Text'''
<div class="actuallycentered">[[File: Sample_Illustration.png|225px|thumb|center|Image description.]]</div>
<div class="infoboxbody" style="background-color: #EEEEEE; text-align: left; margin: 0 auto; padding: 2px 2px 2px 4px;">
Content.
</div>
</div>
For inclusion in MediaWiki:Common.css:
div.infoboxright {
float: right;
width: 270px;
}
div.actuallycentered {
max-width: 320px;
margin: 0 auto;
}
For inclusion in MediaWiki:Mobile.css:
div.infoboxright {
width: 100%;
margin: 0 auto;
}
div.actuallycentered {
max-width: 320px;
margin: 0 auto;
}