I'll take a guess that you've got incompatible sample-rates and/or possibly audio regenerating from more than one source.

I've run into serious audio delay problems before troubleshooting other peoples' rigs that were running analog audio simultaneously to their Sony HXR-NX3 camera and the Blackmagic 4k I/O box. The problem being, the [default 48kHz] audio that gets embedded in the HDMI signal from the camera to the Blackmagic box conflicts with the analog audio they had going straight into the Blackmagic. Recording straight into Media Express, it didn't seem to be a problem. The audio delay only manifested itself on the throughput when they sent an HDMI signal [with audio embedded] out of the Blackmagic box to another unit.

Some variation of that may explain your echo, but sample-rate is usually what would produce the 'slow motion' type pitch shifting.

I don't use Skype, or XSplit, so I have no idea what to look for there.

So, how EXACTLY are you getting the audio in and out from the first device to the last?

Thanks for the response!

First, the Black Magic isn't a box, it's a card plugged into the mobo, specifically, this one:
https://www.blackmagicdesign.com/products/intensitypro4k

So the RODE microphone, guitar, and MP3 player, are all going into the ZED mixer (now properly set up thanks to you guys!) as described in the thread I linked to in my first post.
Then the main XLR outputs from the ZED are plugging into my Canon XA10 camcorder's XLR inputs.
From there, I just take the mini HDMI out from the camcorder and it goes into the HDMI input on the Intensity Pro 4K capture card, so the capture card is the last device.

Then in XSplit Broadcaster, I select no microphone because I select the Black Magic Audio In for the microphone in Skype. And in Skype, I select XSplit Broadcaster as the webcam.

Let me know if any of that helps you out, or if you need more information and I'll provide it to you.

3/15 update:
I turned the main out volume on the rode mic channel all the way down and tested just the mp3 player audio going into the camera, then into the black magic card, and out to the Skype call and it did the same thing on the other end of the call, as in the recording in my original post. There's an option in XSplit to preview the audio and when I use that, it sounds nearly normal, a little stutter but not bad at all. It's only on the receiving end of the Skype call that you hear the garbled-slow-motion-echo sound.

Ok big update here regarding this problem. I discovered it's central to Skype, somehow. I know this because I did the same test using Google Hangout and the audio sounded just fine, no issue at all. So this tells me it's not XSplit, and has nothing to do with the recording setup.

Problem Solved: On advice from Black Magic, I downgraded to an older version of the driver and we only did a quick test so far, but the garbled sound is gone now so I think I'm good to go!