I accidentally stumbled across the following LVS historical company info yesterday. According to this info, as of the early 1930s the following “V” players had pro contracts with Louisville Slugger. Most likely your model originated from one of the following (unless this company info at the time was inaccurate):

Gene Valla
Otto (O.H.) Vogel
Bobby Veach
Oscar Vitt
Ernie Vick

The following image depicts what each player’s facsimile signature would look like when burned into the barrel of a bat:

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Good luck,
Todd