I recently upgraded my OS to High Sierra on my MacPro (late 2013), which has been aggravatingly plagued with the problem described on this board since I unpacked it new from its box in 2014.
Like many here, I tried upgrading the OS, took it several times to the Mac store, upgraded memory, tried different Thunderbolt buses to drive the video, sent diagnostic files to Apple, spent countless hours and emails describing the problem to their tech people, etc. etc. None of it worked. The crashes were always unpredictable and impossible to fix.
Now, I think there is a new fix that is working.
The recently released version of MacOS (High Sierra) supports external GPUs. Not perfectly (I don't think you can have your computer sleep and wake up with an eGPU attached). And, the eGPU boxes have fans, some reported noisier than others. Moreover, you need an AMD card (ideally an RX 580) that supports the Open GL drivers used by Mac. Bitcoin miners drove the price of these cards up by about $80 and sent them into backorder on the market. The backorder problem is solved (although the price is still high).
Apple is sponsoring development of eGPUs, and now offers an external GPU box, an RX 580 8 Gig card, and a bus connector.
https://developer.apple.com/development-kit/external-graphics/
For a late 2013 Mac, you'll also need Apple's bidirectional Thunderbolt 3 to Thunderbolt 2 convertor, plus a Thunderbolt 2 cable to go from the computer to the convertor to the eGPU box. A Display port cable then goes from the RX 580 card to the monitor.
After booting up High Sierra on your Mac Pro, and after configuring you eGPU box, connect the box to your MacPro. After a few seconds, you'll be prompted that, to use the eGPU graphics, you need to log out.
Log out, (making sure you have an active monitor connected to the eGPU box) and then log back in. If all works well, you'll now be using the eGPU box to drive your display. Disconnect any monitors from the D300 or D700 cards, which (I think) have always been the culprit.
I've been going a couple of weeks now. No beach balls. No freezes. No sudden log outs.
I bought my gear to do this months ago, but then sat on it when the RX 580s went on backorder. Here is what I bought:
1. Akito Node Box (~$269.00)
2. Gigabyte RX 580 8 gig card (~$319.00)
3. Apple's Thunderbolt 3 to Thunderbolt 2 convertor (~$49.00)
4. Thunderbolt 2 cable & Displayport cable
Not an investment I particularly wanted to make. And, I think the box supplied in the Apple developer kit is quieter (but also has a smaller power supply). But, the setup seems to have (finally) fixed the problem. And, the RX 580 video card, despite the minor fan noise, is a faster, superior card to the stock D300s found in my original MacPro. You won't get the same performance from the RX580 as you would across a pure Thunderbolt 3 connection. But, it does seem to be better than the native D300s. And, if all ultimately works, it will save your investment in a $4,000 computer.