tracking down the original model could very well be impossible without identifying marks, knowing what speakers were mounted, etc. plus, even if the model was known, availablity is always a concern as it is likely obsolete and not able to be found.
what i would suggest instead is adapting them to use with the speaker mounts they want to use. given that they are plastic though i would not subject them to much weight.
the first thing to figure out is if they are a standard thread. its hard to tell from the photo but they look like they could be 5/8-11 or 3/4-10. once you know the size i'd then get an adapter from that size to the one you need for the mount you want to use (unless you can find one in the size you wanted) and use a circular cover plate to cover the hole.
for example you could adapt it to 5/8 fine thread and use tripod stand adapters like
http
/www.proacousticsusa.com/Products/Frontbms10a20070628170354.jpg or 3/8 microphone stand adapters like
http
/products.k-m.de/media/images/product/19688-300-55_Detail_1.jpg or similar. the type of stand and whats available depends on what speakers you are wanting to install and what kind of mount they accept.
if no type of adaptable mounting solution is available for the speakers they want to use then its always possible to use a cover plate, a generic flange with swivel adapter and drill out a plate to match the one required to hang the speakers or similar diy solution. if done correctly this can look and perform just as good as a purchased piece of equipment
if the plastic threads on the previous mounts are nonstandard then you are in a bit of a bind if diy style work is not something you're willing to do.