Looks like it is indeed a badged Eldredge. I found this:
From Sears, 1880s or 90s. So mine is an updated version of this, I believe, from 1910 and badged differently as "American." Same treadle and leg designs (minus the badge); same drawer hardware, and same case design (I understand many of these were very different). I think the badge would have been again located in that gaping oval in the center of the stand (there's little round holes, like it might have had something mounted there). Still don't know who branded this as the "American" model, but it would likely be Sears or Montgomery Ward, I think...I'll have to question my grandmother about where they ordered most of their things. She wouldn't have been born yet, but they may have only had access to one or two catalogs, as far out as they were.