After a protracted investigation spanning several days (see part 1, part 2, part 3 and part 4), my new home server is finally providing access to my HP Photosmart C5280 printer-scanner combo. The basic goal has been achieved but I cannot be very happy with the end result. To get the printer to work, I had to disable the ulpt and umass USB drivers in the server's OpenBSD 5.2 kernel - they were both being assigned to the device along with the ugen driver the system actually wanted to talk to.
Granted, the ulpt driver is largely superfluous when the printer works with ugen (though I can imagine having another USB printer to which I'd want to print through a service other than CUPS that would specifically need ulpt). Disabling umass is more serious. As it happens, my home server needs no USB storage at the moment but that could change in the future, putting me in a difficult spot. I don't think this is an acceptable state of affairs in the long term, especially when the previous home server running OpenBSD 4.8 exhibits no such limitations.
Regarding the effort it took me to get to this point, it was largely a function of my insistence on figuring things out on my own. I do enjoy this sort of detective work from time to time and I did learn a bunch of new things so it was definitely time well spent. Truly resolving the issue is beyond my capacity, however. It's a task for OpenBSD hackers who know their way around USB plumbing.
UPDATE The issue has been fixed in OpenBSD 5.3 which was released on May 1, 2013.