Making "off-topic" board free of signatures won't solve the problem. Most of the posts there doesn't contain signature.
Seems that some people post there only for increasing their activity. (I don't know what is the benefit of high activity when the user doesn't have any merit)

I counted the posts that contain signature in the first page of all four topics you mentioned.
Only 11 of the 63 posts contain signature.

I have some additional ideas, like make restrictions like in the Ivory Tower, so no posts and activity are generated from posting in that section then the spam will Suddenly disappear from there, and all those account farmers will have to find a real job .