It is going to be difficult to prove where this maverick is from, but start by looking in local city directories for a pool or billiard hall operated by two people whose last names start with T and W in the 1915-55 timeframe. The 2½¢ denomination was typically used by pool halls. Do post it on tokencatalog to get more folks to look at it. It is not in Smith's MO token book.
John in the Great 208