Actually, I checked in config.inc.php and discovered that the ATTACHEMENTS_PATH did have the "stripped" value. I tried to give it escaped slashes (e.g. "\\") and it didn't like that. So, I changed them to forward slashes (e.g. "/") and it seems to work as expected now. They even show up fine in the control panel now, although I've not tried to change them there again as in the brief time that I had changed it, it generated support issues as people's uploads were not occuring.
On that note, I got calls that downloads were failing (people upload screnshots for support purposes.) With the bad path, it appeared to the end users that the uploads were working fine. Meaning, they weren't being made aware that their file didn't really upload. It was obvious that it failed though when someone visited the post to assist, and the download couldn't be found. I can see a gap in numbers in the attachment directory during the time that the uploads didn't work (e.g. the files went from 4510.png to 4522.pdf, with nothing inbetween but "test.file".)