@Scot Gould 

Now that the crashing problem is fixed, I've tried to view the eps generated by Maple through EPSviewer as you have, and it seems that the files are readable. The remaining issue might be a LaTeX compiler problem, perhaps due to how large the file is. My current workaround is to save it as a PNG in Maple, and then use an EPS converter to put it into EPS format. Quality is well-preserved. Oddly, it's almost quicker to do that than to save it as an EPS from Maple.

@mikerostructure 

Thanks for trying that. I really appreciate it. I guess it's an issue with plot3d EPS files more generally (2D files work fine). My reason for saving that way is that I'm used to them playing well with LaTeX. 

The green upload arrow won't accept .eps files, unfortunately, so I can't attach the plot.

I appreciate all you've done to guide me around this problem. I'm comfortable calling the issue mostly resolved. I guess I just need to say goodbye to ye olde EPS file format, which is not the worst outcome.

@mikerostructure 

Update: I updated to an optional graphics card driver (I usually avoid these until they're official), and it seems to have fixed the crashing issue. That said, Maple still cannot save files as an .eps without corrupting them. PNG, BMP, SVG, and other file formats are fine.

Still, this is an improvement, nonetheless! 

@acer 

Thanks again for taking your time with this problem. I see what you mean, now, re updates.

Re: updates. I can't really pinpoint at which point plot3d started crashing. The last time I used this function was in 2018, so that was many updates ago. Here's the best timeline I can provide.

April 6, 2020: I started the offending file using Maple 2019.2, and was having a problem saving the renderings as an ".eps". I could save the files, but the resulting files would always be corrupted an unopenable. 
April 11, 2020: Updated to Maple 2020. The saving problem is now a crashing problem, where the program crashes when I right-click the plot3d rendering. 
April 13. 2020: Problem still persists. Created a new file to try simple plot3d functions (as in original post), and the same problem from April 11 continues.

Re: Colleague's attempt. My colleague is on Maple 2019.2. I sent him my Maple 2020.0 file, from which he attempted to render and save the plot. His Maple 2019.2 does the same thing that mine was doing on April 6, generating corrupted files. I have asked him to try to render and save the simple partial circle plot from the original post, and those files too are corrupted. He is also on a Windows 10 machine. 

@acer Do you have 2020.0? I know you might not have the time for this, but if you made a simple plot3d plot like my example above, are you able to export it by right clicking it?

Update: I have also re-installed Maple 2020.0, and the issue persists.

@acer 

Thanks for the suggestion! I'm on Windows 10 Pro. Just did a small update, still no change. I had a colleague try the same thing on his (also Windows) computer, using Maple 2019, and the outcome there is that the files go through the "saving process", but extremely slowly, and resulting files are corrupted. I'm on an AMD Radeon R9 270X graphics card, and that is also up to date. 24GB RAM and an i5-4690K, if that's also useful.