Problem is solved. Wasn't Parallels after all, though it may be related to Parallels tools.
Breakthrough came when I was measuring memory usage in Windows while running QGIS, looking for a memory leak. Didn't find one (Windows usage was completely flat) right up until I got a memory full error from OSX. So clearly the problem was on the Mavericks side.
Ran Activity Monitor.app on Mavericks. Ultimately, showing All Processes, found a process called photosmart (presumably an obsolete driver for my HP photosmart printer) that was allocating about half a gig of memory per minute for no reason, and ran continually, ultimately stealing all of my application memory. This is a 24GB system, and Parallels is allocating 16GB to Windows7 when it runs. So it simply was running out of memory faster when running Parallels, which is why it seemed to be the culprit.
The AppleCare technician I was working with can't actually find where the driver is (the file isn't obvious when doing a spotlight search). He's escalated it to Apple Engineering, and we'll presumably find it when they respond. For now, as a workaround, whenever I log in, I open Activity Monitor, click on All Processes, double click on the photosmart process and click on Quit, selecting "force quit". That shuts it down for the session and my memory usage drops to a normal level.
When I went to see if I could use the printer, I found there was a parallels print job that was trying to run.... I don't think I've ever tried to print from parallels, there it was. It's now deleted. That was maybe why the job was continually allocating memory.
Last edited: Mar 27, 2014