I can't recall the amount of plies or whether it had re-rings, or even the color. I got that tom with a Gretsch set and looked at it long enough to pack it and send it to the person I sold it to.
I do seem to recall that the buyer said he had a KENT snare that the floor tom matched, which is why he bought mine. So that wrap or a similar wrap may have been used by more than one company.
Sorry I can't answer your question re the missing badges. I only really know Ludwig and Gretsch.