I cobbled this userscript toether with some basic jquery/javascript. It adds in a clickable "Random Mode" toggle that transforms the content area into a slideshow utilizing e621's built-in "Random". You can use it pretty much anywhere on the site, and doesn't change your location.

In essence, it loads the page using "Random" and strips it down to just the image, then displays it with a very simple form of double buffering (though the effect might not be very pretty based on image load time). I'll be tweaking it constantly over the next few days till I feel satisfied with it, right now it's very hacked together.

https://userscripts.org/scripts/show/173307

You can press [Space] to pause the slideshow. I need to figure out how to get the images to resize. You can also customize the slideshow time by setting the "mTimeoutInterval" variable in the script. I should add in a user front-end textbox for that or something.

I'm also up for suggestions for features and changes. Please let me know what you think of this. <3

p.s. You'll need Greasemonkey or Tampermonkey for this.
p.s.s. If you can't find the random mode toggle, it's right below the top navigation bar. It's white and bolded.