Turns out my HP ProBook 6360b supports this just fine. It’s just a question of enabling the EFI boot capability – an option which, if you’ve got it, is generally buried in the BIOS menus. HP’s instructions for a slightly different system are here – they were helpful in confirming what I was looking for.
Some Microsoft folks describe how to install Windows 7 on a UEFI Dell laptop here – again, it’s essentially the same sequence. Additional instructions from Microsoft are here; the instructions there that applied in my case were the “Boot from file” ones. There’s also a Microsoft whitepaper here which gives a short background, including one notable rationale for trying for a UEFI install if you’re planning on running 64-bit Windows anyway: you’ll probably get faster boot times. (Also check out the the UEFI Wikipedia page.)
Once the system is up, here’s what you’re looking for in bcdedit.exe to know that you did it right: