You should also be aware of the Florida Digital Newspaper Library operated by the University of Florida at
http://ufdc.ufl.edu/fdnl1. Just do a search for Tampa. It has very old issues (1800s) of Tampa papers plus more recent copies of local Black, Hispanic, Catholic and Jewish papers. The coverage is by no means complete. Also, local historian Julius Gordon created indexes to several old Tampa papers. They are available online a the the USF Library. Just do an author search for his name. Finally, don't overlook the St. Petersburg Times (now the Tampa Bay Times). It carries obits for the whole area.
Steve