Hi David,
Oops, sorry I should have mentioned this in my first reply above: If you repurpose an old Map Tour to work around the bug that was introduced in tours created after June 26th, you have to use a Map Tour that does not use a hosted feature service behind the scenes, i.e. a tour that is not created by uploading images directly into the Builder (because that workflow uses a feature service in which the images are stored).
The reason for this is that feature services impose their own, stricter set of supported HTML rules, and this does not include Audio. This is what is giving you the message about the invalid tag when you try and save. Map Tours that use images uploaded into the builder have never supported tags like Audio and Hr (this disparate HTML support is a peculiarity of Map Tour that we don't like and that we won't be carrying forward in our future dev plans for this app) and don't let you save the tour until you remove any unsupported HTML.
So if you repurpose an old Map Tour to work around this issue, it has to be a tour that references its images from Flickr, Google+, or directly via URLs (either URLs entered manually in the Builder or via URLs included as data in a CSV file uploaded into the Builder, or via URLs included as attributes in a CSV, shapefile or feature layer added into a web map that was then published as a Map Tour. Use the audio embed code from the blog you referenced, not the code that Alison posted above. So I am pretty confident that the Map Tour you are trying this workaround with uses uploaded images. Sorry about this extra hoop. Note that you can't change an existing Map Tour that uses uploaded images so that it no longer uses them, because this option is chosen at initial create time.
I'm hoping you can find an older tour to work with that doesn't use image upload. Another alternative would be to use Story Map Journal for your tour-type story. Using Map Journal lets you present multiple images, embedded content, including audio (using the code that Alison posted above) and unlimited narrative text, and so can be a great way to make more detailed tours. There are some examples in our Gallery (click this link for examples). Out-of-the-box Map Journal doesn't support clicking on a point on the map to go to the section about that place, but if you need that it can be added via some customization.
Rupert