There was always issues with large images in Processing. Java is quite memory hungry, and restrictive at the same time, at least with the 32bit version. The 64bit version, perhaps in server mode, might have less issues (with memory; there are issues with native libraries, sometime).
I still have a good old 32bit Java (on Windows 7 64bit), and I was able to load such image with Processing 1.5.
A 6000x9000 pixel image uses approximatively 205MB (counting 4 bytes per pixel; if really using 24bit colors, it should be 154MB), so it is reasonable by modern standards.
I tried to up the PDE memory to 512 but I got an OOM exception. With 1024KB, I was able to load the image (some random image I just resized and saved to Jpeg format).
Note also that some processes, like decompressing the Jpeg data, can eat more memory than just the storage of the final data. That might explain why we need memory to be nearly three times the image, and I haven't used stuff like loadPixels that increase the memory usage!
In short, perhaps try to use a 64bit Java... And report your progress here, please, I am sure this interest lot of people.