Ok, Tom. Following up with the union negotiation angle I pm'd you on your granduncle and thinking along the lines that the box could have been a gift from either the union(s) or the city of Tampa (given that the box was specifically made for him), I narrowed my search to the years of 1910 to 1945 figuring these would be his most active years as far as his career goes (age 25-60).
Unfortunately, the database I use can only search major national newspapers and not the smaller regional or local papers.
The years I searched were generally labor dispute free with the few exceptions noted below. None of these mentions a federal mediator but it seems likely that one would have been involved and it possibly could have been your granduncle. Either way this gives you some date ranges as to when the box may have been given to him.
OPA SUES CIGAR MAKERS :Action Against 11 in Tampa Asks $1,858,652 Damages. (1945, June 29). New York Times (1857-Current file),26. Retrieved January 4, 2009, from ProQuest Historical Newspapers The New York Times (1851 - 2005) database. (Document ID: 306096732).
Lastly, one significant event that occurred involving the Tampa cigar industry and the Federal government was summarized in this article from 1903 although your granduncle would have only been 18 at the time, so it is unlikely he would have held a high enough position at the time to get involved had he even worked for the feds then. It is possible however that an event of this type made it necessary for the feds to keep an eye on the cigar unions moving forward and thus could have been an impetus for your uncle to make periodic trips to the Tampa area. (all entirely speculation on my part, of course
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APPEAL TO THE PRESIDENT :Members of Tampa Cigar Workers' Union Warned to Leave the City.. (1903, March 13). The Washington Post (1877-1954),1. Retrieved January 4, 2009, from ProQuest Historical Newspapers The Washington Post (1877 - 1992) database. (Document ID: 259164092).