Okay, so I did a few things and the problem appears to have been resolved thus far! At least, I haven't had it occur today and it normally would have by now, so I'm posting this to see if anyone else can replicate my success.
I was especially interested to note that you also had Microsoft Office 2011. How many others here have that installed?
Unfortunately, since I wasn't really expecting to succeed, I didn't isolate these steps and cannot say for certain if any of them was the one to address the problem.
Uninstall Creative Cloud
I had a long expired Adobe Illustrator trial, so I removed Creative Cloud (good riddance) and Illustrator. I have no idea is this is relevant, I'm just reporting what I did.
I actually suspect this one is not relevant, but who knows, I did it so I'm writing it.
Remove Microsoft Office 2011 (then install Office 2016)
Due to the Microsoft fonts and the somewhat broad spread across OS X an Office 2011 installation has, I now suspect the cause of the problem has to do with the interaction of something to do with Microsoft Office 2011 and El Capitan.
Instructions to DEEPLY REMOVE Microsoft Office 2011 are here: https://support.microsoft.com/en-us/kb/2398768
For the convenience of those comfortable with the terminal, I saved a log of myself following this process via the command line (quicker than doing it in Finder). WARNING: Contains sudo rm -rf commands, WHICH ARE BASICALLY ALWAYS DANGEROUS, use at your own risk, if you aren't sure what you're doing DO NOT JUST BLINDLY COPY AND PASTE THIS, please follow the Finder-based instructions in the link above instead.
sudo rm /Library/LaunchDaemons/com.microsoft.office.licensing.helper.plist
sudo rm /Library/PrivilegedHelperTools/com.microsoft.office.licensing.helper
rm ~/Library/Preferences/ByHost/com.microsoft.*
sudo rm -rf /Library/Application\ Support/Microsoft/M**
sudo rm -rf /Library/Application\ Support/Microsoft/Scripts/
sudo rm /private/var/db/receipts/com.microsoft.office.*
sudo rm /private/var/db/receipts/com.microsoft.office.*
rm ~/Library/Application\ Support/Microsoft/Office/*
rm -rf ~/Library/Application\ Support/Microsoft/Office/*
rm -rf /Library/Fonts/Microsoft/
sudo rm -rf /Library/Fonts/Microsoft/
rm -rf ~/Documents/Microsoft\ User\ Data/
sudo rm -rf /Applications/Microsoft\ Office\ 2011/
Note that a Microsoft Fonts folder is removed as part of this process. So even though I had already tried this, I did the following once more:
Fonts
Clean up fonts as recommended in an earlier post by Diane. Open /Applications/Font\ Book.app, click a font to set focus, do Edit->Select All, then click File->Validate Fonts, delete what it suggests)
Then clear font cache
sudo atsutil databases -remove
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After all this I rebooted, and then I installed Office 2016 instead of 2011 (since unfortunately I do need to collaborate on Office-based projects at the moment, I couldn't really leave my system completely Office-free to test, so I compromised by getting the new and presumably more El Capitan-tested version)
I will try and update after some more time passes, but I'm posting now so others can try this out.
Like I said, I did everything at once, so I can't be sure what the magical step was, but I suspect it's related to Office 2011. Help others, report back if you have 2011 and can try uninstalling it! (Also post if you're experiencing these problems and do NOT have Office 2011 or even any Adobe CC software. It's also possible that this hasn't really fixed anything at all and it's going to crash five minutes after I post this, it's also possible there's more than cause of PDF hanging that might not all be exactly the same bug, etc)