Well, it does look like the repeater I found on google patents, and as I said in the other thread, it appears to be a fairly complicated devise- at least compared to many others I've seen.
http://www.google.com/patents?id=S8ZcAA ... SA&f=false
For this reason, I assume it would have been pretty expensive to manufacture & to buy, so they may not have sold as well as many others.
Also, to my uneducated eye, it appears that a lot could go wrong with such a complicated mechanism, which might explain why yours was removed & discarded at some stage, and is perhaps why no-one here appears to have come across one (so far).
Personally, I think it's nice to have machines with original accessories, even aftermarket ones such as these, that were fitted by original owners back in the day.
Like you, I would probably also attempt to hunt one down for the machine (if only to use the redundant screw holes that are now on the motor board).
I guess the obvious place to look is ebay, but you'd have to check constantly I think, and it could literally take years of looking before one actually surfaced.
If any of the phono-shows are handy to where you live, they'd be a great place to search as well.
I'm not sure if the "Re-Pla-Stop" name actually appears on the item itself (I would assume it does somewhere), but if not, non-collectors may not even realize what they have is a record repeater, so it might be worth looking in other sections of Ebay apart from the phonograph section, although I cant really advise which sections, as our ebay catagories are much less specific than those on US Ebay.
I guess I would check anything to do with mechanical antiques/collectibles.
Good luck with your search, and if you are ever successful, I'm sure we'd all be interested in seeing the actual devise. It would be especially nice if you post a video of it in action on youtube

Good luck again!