Using Henne to finish the season is a mistake. Think about it: you know what Henne can provide. He's a low-end QB that's good for 6-7 wins if you have a good defense. Every now and then he might have a great game but there are too many crummy ones in between.
With Gabbert, it seems like the writing is on the wall, but it's still worth playing him. One of two things will happen. Either he'll continue sucking and help guarantee the Jags a top 2 pick, or he'll start playing well and be the QB they always hoped he would. That's a win/win. Playing Henne won't help you find the QB you want and it may knock you out of the top 2 picks.
They've intentionally avoided Freeman, Cassel, and Flynn to this point, who would all be upgrades on both Gabbert and Henne. They're aiming for next season because they're obviously tanking.