Well, turns out STP have found their guy, and it's this guy…
Entertainment Tonight reports the band have recruited The X-Factor contestant Jeff Gutt (pronounced "Goot") to be their vocalist. Gutt, who also appeared on season three of American Idol, has been working with STP for a few months now according to the report, and based on the above video, he can definitely sing. So it will be interesting to see what the final product is.
Update: Since originally posting this, the ET article was updated with a statement from the band denying they've confirmed Gutt as their vocalist, saying “The band has been rehearsing with several singers over the past few weeks. They haven’t made a decision yet.”