Hi there, @klwhiteside ...
I was wondering if that was what you were doing...so thanks for confirming your steps. In trying to replicate exactly what you were trying to do, I noticed the same behavior where any video was aligning to the left side of the page. But, I'm wondering if this is really that big of a deal anyway. Why do I say this? Well, if you were to save the page and view it the thumbnail of the video will still be left-aligned...but when you actually play the video, it takes up the entire space of my screen. So, I really cannot tell one way or the other if the video is centered on the page when it starts to play. I suppose I could modify the HTML slightly so that it was something like:
<p style="text-align: center;"><a id="media_comment_m-5QckVS6cJPvpr1..." class="instructure_inline_media_comment video_comment" data-media_comment_type="video" data-alt=""></a></p>
Here, you can see that I've added in style="text-align: center;". However, that still doesn't place the thumbnail on the center of the page as you'd like it. What I did notice, though, is that when I clicked the play button on the thumbnail, I briefly saw the video move to the center of the page, but then it went full screen again.
So, while I understand there might be some good reasons why you'd want your videos to appear as centered on the page design-wise, I'm not sure there is anything else that can be done. That's why I'm going to share your question with the Canvas Developers group here in the Community in hopes that someone with a bit more HTML knowledge might be able to tell us if this is possible or not. If you are not yet following this group, you can use the link that I have provided, and then you will see two buttons at the top right corner of the screen. Click on both "Follow" and "Actions". (You'll have to further select "Join group" from the "Actions" menu.
I hope this will be of help to you, Kim.
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