HP 5500 rejects custom paper size

Got a package of badge stock sight-unseen. Says Avery 74520 on the box,
but 5384 on the sheets. Sheets are 11" by 4.25" (of which the 0.25" is
a perforated, strip at the edge, obviously to add strength & remove
after printing). So this is a single column of 4-inch-wide badges.

We can't get the printer to accept it. Only the manual-feed tray could
be expected to, as the adjustments on the others don't come inward that
far. But no matter what we try it prints either nothing or a single
graphic line which appears on every badge. Setting a custom paper size
(in Word, on the printer, or both) doesn't help. When the printer gives
a message at all, it says 41.3 unexpected size in tray. Asking it for
help says to be sure "the switch" is set to Custom Size.

There's no switch on that tray.

What are we doing wrong?

I can probably print these 8 badges at home on my crappy little Canon
but I'd like to know how to run next week's 6 dozen them on the mammoth
at work.

I'd check the manual if it were anywhere on this planet. ;(

Thanks for any clues.
MT