If you are carving and carving correctly, you will accelerate through your turns not slow down. One of the thing to work on here is making your edge change sooner; before the board crosses the fall line. When you rock onto your downhill edge early so that a person above you on the hill can clearly see the base of your board, you will explosively rocket though your turns.
One of the most difficult things to do when you want to do high speed carving is to not skid at the bottom of your turns. One thing in your statement provides some clue to where part of your difficulty lies. You said you are leaning into the turns. While this is a great start for basic carved turns, it will never allow you to generate the speed you are desiring. For that you must progress beyond inclinated, basic carved turns in favor of angulated dynamic carved turns.
In a dynamic carved turn, you do not lean the body to tilt the board onto its edge, you use the ankles, knees and hips to tilt the board while you maintain a quiet upper body over the top of the board. In addition, the use of down unweighting to make the edge change as opposed to up unweighting is a key component. You want to eliminate any maneuver that adds drag and pushing against your board to pop off the snow in an up unweighted maneuver robs energy which equates to speed.
Back to avoiding skid at the bottom of your turns..... The reason everyone skids at the bottom of any turn is because this is where all of the energies developed throughout a turn all come together. You have your momentum down the hill, gravity pulling you down the hill and centrifugal forcing pulling you to the outside of the turn. If you are using an inclination in your carving technique, you will be too stiff and erect to have the required "light touch" to prevent the edge from breaking loose at the bottom of your turn.
Now, if you work the top of the turn better by switch to the downhill edge early and setting that edge hold good through angulation, you can then extend slowly at the top of the turn to precisely regulate speed early and as your enter the fall line, you begin to flex through the bottom of the turn. this allows you to reduce some of these forces at the most crucial point in the turn and absorb any chatter that can break your edge free and create skid. Even a little skid will turn a carve into a "scarve" and that will scrub a lot of your speed.
So, start playing around with dynamic carving and get proficient at it. Then, you will feel the thrill of rapid acceleration through your turns while still having control of your board....