So I downloaded Apple's HP drivers for 10.6 from http://support.apple.com/kb/DL907 and installed them on the single 10.6 machine we have in the group (the previous attempts at this were on 10.5 machines with Apple's 10.5 drivers).
Installing those drivers let the 10.6 machine properly determine the correct printer model when installing it.
Looking at the package receipt (and http://support.apple.com/kb/HT3669), the 10.6 drivers do include a printer description for the HP LaserJet P2035, but it is not there in the list for the 10.5 printers ( http://support.apple.com/kb/HT1893).
So why are the 10.5 machines only installing the printer properly when connected via USB? Does the printer have an internal PPD copy that it can only distribute via a USB connection? Or how can I get a copy of the PPD for 10.5 (the 10.6 PPD points to paths that don't exist on the 10.5 machines (/Library/Printers/hp/laserjet/hplaserjetzjs.bundle/), so I doubt I can just copy the 10.6 version and have it work properly.