Sadly, this tale does not end with me being able to get the part I needed, but, BUT, the folks at HPPS tried really hard to help me, and sometimes that counts just as much as getting me the right answer. I spent about an hour-and-a-half in their showroom over a couple of days, the first day with the broken faucet and the second day with pictures of the parts that are still attached to our house. (Note: I could have emailed them the pictures, which is what they asked me to do because that would have been easier than asking me to come back into town, but I was in town anyway, so it was ok.) Over those two days, the staff at HPPS dug through their warehouse; made phone calls; looked up information on line; tracked down the veteran guys in the office, who have been around and seen some things in the plumbing world, to try to identify my mystery faucet; thumbed through catalogs; and generally tried to provide some actual customer service. Also, they managed to use the term "nipple," which is a vocationally legitimate term, in a relevant manner without snickering; and, let's face it, unless you are in the medical or body-piercing field, that's not always easy to do. But, I digress.
The end result: I now know that the piece I need has been obsolete since 2002, and I will probably have to call a plumber to fix our situation. That's a drag, but the fact that they didn't make me run all over town to 6 different plumbing supply places and make 14 different phone calls to find out the same information meant a lot! Because that's the level of customer service I've come to expect these days. Has anyone else noticed this? Is it just me or do you find yourself doing more and more of your own leg work these days in order to help Customer Service do their job, things that Customer Service used to do in order to provide, you know, service to their customers?
Anyway, thanks to Justin, Jeannine, Courtney, and the rest of the folks at Hawaii Pacific Plumbing Supply Company who helped me identify the latest obsolete part in my house! (You guys wouldn't happen to know if there's some place that carries screen doors that are about 1/2" smaller than everything that seems to be in the stores, would you?)