I'm not sure if perhaps an update to Muse caused this issue to be fixed, but I was able to use the iframe method to do this just a couple of days ago.
I didn't go read about it at some forum; just figured it out myself from learning about youtube embeds on Muse pages. All I did was insert an HTML code (just copy the code from a text editor, go to Muse, and hit paste) into the Muse page:
<iframe width="1000" height="450" src="...yourblog.tumblr.com" frameborder="0"></iframe>
Adjust the width and height as needed and the URL to point to your blog in the text editor beforehand, and that's it! After that, I went into tumblr's CSS customize mode and changed its background color and font colors to match the site I was creating the iframe for.