More focused air and higher tongue position are very good and important advice, but depending on the player and the general style there's only so far you can go before it starts to be detrimental to your playing. Tongue position does affect things including how different registers respond.
I think a good way of thinking about it is in terms of working from a happy medium. It is very good to have a flexible sound, and different mouthpieces will lend themselves to be more suitable (depending on what you want to sound like).
There are different routes you could go with mouthpieces, and trying out different ones always is very helpful. From a hard rubber piece like yours, you could go to a hard rubber piece with a higher baffle (more edgy), a metal piece (more lively), or a metal piece with a baffle (industrial strength mouthpiece, so to speak...). I am a recovering mouthpiece addict, but going through that entire process has really opened my eyes to things.
Buying expensive mouthpieces is cool and all, but it really starts to get to be a real strain on the pocketbook. When you start looking at these high-dollar mouthpieces like the Sugal, it's really helpful if you can try one out to get the general idea. Also VERY important with them is... they're pretty inconsistent, and even at a $600+ mouthpiece, he still pushes ones out that need to be worked on (which I think is irresponsible as a mouthpiece artisan). One huge plus with them is that because of their unique design you can get a pretty unique tone quality. The Super Gonz II that I own has a fairly high baffle, but is also a pretty wide mouthpiece with gives depth to the sound while still having quite a bit of edge. So in short... if you go for a Sugal and get a good one, it's a really great mouthpiece.
The mouthpiece that I play on right now is a Jody Jazz DV, and one really fantastic thing about that company is they give you a trial period to use the mouthpiece before it's all said and done. But you play on one, so you probably know that.
If you wanted to go all-out with edginess, some good pieces to look at would be a berg larsen (I don't personally like them though), a dukoff, or some of the guardalas (MB and King/Super King models come to mind).
One other route you could go is talk to someone like Keith Bradbury (MojoBari) or Dave Jary - guys who work on mouthpieces and do a lot of refacing work. These guys can make absolute magic out of mouthpieces, and even just talking to them you can get some really good advice and information about your tastes and particular setup.
There are a lot of different things you can do, and I guess from here it's just trying out things and asking questions. As the saying goes "You can lead a horse to water, but you can't make it drink the water" ...unless you force the water down it's throat, but then is the horse really happy?