I just had a chance to boot into Fedora 18 and test GIMP 2.8.10. To my surprise, I had no memory issues or crashes in Fedora 18. In my first test, I extruded to a depth of 500 layers, with no problem. I didn't bother testing any further. Obviously, there is some kind of corruption in my Fedora 19 installation and the crashes I'm experiencing in GIMP are not inherent to GIMP 2.8.x.
I had been noticing quite a few random crashes in Firefox, over the last few weeks, but I didn't think much of it, until now. I suspect whatever corruption problem I have in F19 is causing Firefox to crash, as well.
ek22, sorry that I couldn't duplicate and confirm the problem you're having with GIMP 2.8. You might occasionally be hitting a 2.8.x bug with your large images.
A big thanks to everyone who offered suggestions to help me figure this out. I'm glad it wasn't a GIMP problem, after all. I can reload a corrupt Fedora installation easy enough. Shoot, it was time to move to Fedora 20 anyway.
I'm marking this topic as solved.