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It is possible to test the speed of the Chromecast actually. You need an Android app like Web2Cast ( https://play.google.com/store/apps/details?id=com.rabidgremlin.web2cast&hl=en_GB ) And you can then just cast https://fast.com directly to the Chromecast using the app. This is not screen casting, this is loading a very app on the Chromecast which loads the target site inside an iFrame so that the Chromecast itself is running the code.
EDIT: I just checked it to make sure it still works and it does, but when you cast it you will only see the Fast Logo at the top of the screen, you need to press the Scroll Down button in the app several times to get to the actual speed figure (on my Gen2 I'm reading 15Mbps) on my computer I'm reading 56Mbps.
Create your slides show from a folder on Google Photos or Dropbox here: http://dakboard.com/
Cast that URL to your Chromecast using this app: https://play.google.com/store/apps/details?id=com.rabidgremlin.web2cast
There are a number of options - from an Android Device for example you can cast actual webpages using https://play.google.com/store/apps/details?id=com.rabidgremlin.web2cast&hl=en_GB or you can write your own Chromecast app which is really really easy using https://github.com/googlecast/CastHelloText-chrome as a starting point - you can simply stick an iframe on the page and load any website you like inside it - the only thing to be aware of is that the app must be hosted on a https connection if you want to load it on any Chromecast that isn't registered as a developer device for that app.
This is what I use: https://play.google.com/store/apps/details?id=com.rabidgremlin.web2cast
By the way I just found this app, might do what you need https://play.google.com/store/apps/details?id=com.rabidgremlin.web2cast