So, here’s the code for either one:
<object type="application/x-shockwave-flash" data="[INSERT VIDEO URL FROM EMBED CODE PROVIDED HERE]" width="400" height="326"><param name="movie" value="[INSERT VIDEO URL FROM EMBED CODE PROVIDED HERE]" /><param name="FlashVars" value="playerMode=embedded" /></object>
Took a while to figure out, but it works. I originally tried the code mentioned in this article, but it kept breaking my site, so I trimmed it all down to the bare essentials. This works for me and my template. Let me know if it does / doesn’t work for yours in the comments. w00t!
UPDATE: Great post from Ryan over at Hapless band of staff and regulars, where he tweaks my code slightly to avoid YouTube upscaling of the video. Check it out.