Thank you, Thomas. I was afraid that was the case. Sadly, even after increasing the maximum memory available to yEd to 1500MB with the -J-Xmx1500m option, I still get an out of memory error when exporting to PDF. Perhaps there is some problem with the way my company manages settings in the operating system that is preventing yEd from getting the memory it needs.
It's ok if the PDF is large, but the exporting step causes an out of memory error. It is too bad that the image file must be loaded into memory all at once, rather than reading and writing a few rows of pixels at a time.
Also, if the entire image wasn't loaded at once, the export to .gif from yEd would then result in a small (~1MB) file. I suppose the underlying image libraries cannot be changed though.