1. On the website as admin, turn OFF the multimedia filter.
2. Create a new File using a short .mp4 video clip. (Apart from the name and file, leave all other settings default.)
3. Right click on the video and copy to clipboard the URL of the mp4 video file.
4. Create a Page with the following html, including the URL from above:

<video src="URL" controls></video>

Now check it on an iOS device (I'm using an iPhone 6 currently on IOS 11.4).

5. In the app, log into the website and go to the course.
6. Open the page. Check that the video plays correctly.
7 Turn off the internet connection / wifi on the device.
8. Leave and reopen the page. Check that you can still play the video.

Testing existing videos
1. Go to the 3.4 site
2. Open the MM Dev Test course and go to Section "Resource: Page"
3. Check that all the video resources there work as expected

In terms of label tags (or any code that will be treated with core-format-text), the workaround appears to be quite simple; just use the 'source' tags instead of src. For example, instead of:

<video controls src="https://example.com/video.mp4"></video>

you can do

<video controls>
<source src="https://example.com/video.mp4" type="video/mp4" />
</video>

When doing this in code, the workaround is to do the above, but also change the 'src' attribute to 'target-src'. You then also have to add the normal core-external-content attributes, to the source tag not the video tag.

<video controls>
<source target-src="https://example.com/video.mp4" type="video/mp4" core-external-content component="whatever" componentId="whatever" />
</video>

This seems rather weird, but appears to work.