I believe that the roots of your problem are evident from your description of how you turn. I suspect some technical, and some tactical, issues. Let's take a close look:
First the technical stuff. There MAY be a subtle, but critical, understanding issue here. You wrote, "When I think of making a turn I think of extending my body upwards and putting most of my weight on my outside ski." Think carefully about what you mean by this statement. If you extend "up," and shift your balance to the uphill ski at the same time, you are very likely moving your body UPHILL, and OVER your uphill ski. Of course, before you can turn, like a bicyclist, you must be leaning into the turn--not directly over your balance foot. So what do you do? PROBABLY twist that uphill ski tail farther up the hill, out from underneath your body. Voila--a wedge! And perhaps more importantly, a skidded entrance into the turn.
This sequence is known as a "rotary pushoff." I'll bet that, during that "up" extension, you also rotate some part(s) of your upper body into the turn. It may be subtle--perhaps just your hands, and only slightly. But I'll bet it happens. And I'll also bet that your downhill ski edge is engaged during this "up" move, before you transfer your weight from it. If so, it cannot turn down the hill as you start the turn with your uphill ski--again resulting in a slight wedge as you initiate the turn--a quick "1-2" action of your legs and skis into the turn.
The key to changing this involves several things. First, as Rusty describes, you must think of starting the new turn by letting your DOWNHILL ski tip turn DOWN the hill (or actively turning it down the hill). And, of course, your body must go down the hill at the same time if you want to stay in balance. This is almost the opposite of the "extend my body uphill and [transfer the weight to the uphill ski]" move that you described!
DO NOT try to transfer your weight, especially prior to the turn initiation--it simply causes you to move in the wrong direction! Instead, focus on turning your skis into the turn, ALLOWING the weight to transfer toward the outside, as it does when you turn a car. Depending on your speed, the accuracy of your movements, the radius of your turn, the conditions of the snow, and the steepness of the hill, the "full" weight transfer may not occur until half-way through the turn--if ever! And it will occur as RESULT of the turn--not as a cause. With improved movement accuracy and increased speed, that weight transfer may well occur quickly, completely, and early in the turn, but it will still be primarily the turn's result, not its cause.
The "extension" will also occur as a side-effect, rather than an intentional action. In order to turn that downhill tip down the hill, you will have to release its edge grip on the mountain. This involves reducing its edge angle, which also requires a movement of your body DOWN the hill, beginning with a tipping of your downhill foot and leg down the hill. A slight extension of your body will probably accompany this relaxing of the edge angle, but again, it will RESULT from it, not cause it, and it will be directed DOWN the hill, not "up."
Now for the tactics. All of these movements assume that you actually want to GO down that hill, of course! They assume that you want to GAIN speed, too, not lose it, when you start the turn--because that is obviously what will happen when you let go of the mountain and point your skis down the hill!
You said two things that make me suspect otherwise: "I like to ski relatively fast," and "I...turn to control my speed." Remember that "fast"--relatively, or otherwise--is a state of mind. It is usually the state of mind that means "I do NOT want to go FASTER." Like I said, you MUST want to go faster when you start a turn, because that's what will happen, whether you want it or not, unless you put your brakes on (read "snowplow"). Skiing "fast" puts you in a defensive state of mind, which makes these very OFFENSIVE moves unlikely, even you have the skills to do them!
And "turning to control speed" confirms my suspicion. Great turns control DIRECTION--not SPEED. BRAKING slows you down. Great turns result from "GO thoughts"--the offensive intent to GO THAT WAY, rather than the defensive intent to slow down, or to "stop going THIS way."
Of course, GOING--uphill--also slows you down (whether turning, or going straight). So these offensive "GO" turning movements, because they give you precise control of your line, will ALLOW you to go uphill if you choose, but not usually until the end of the turn. When you START the turn, you must want to go DOWNHILL, and to GAIN speed!
Learning to think of the turn as a direction-control thing, rather than a speed-control thing, could well bring about a quantum leap in your skiing, not to mention solving your "snowplow problem." I do not use turns to control speed. I use them to control LINE. And I ski a line that eliminates the NEED to control speed--a line that quite often carries me uphill. Only if I don't have the option of skiing this "slow line," will I use my brakes to control speed.
While braking involves some similar movements to turning, it is really the OPPOSITE, both in technique and in intent. A "braking turn" (a self-contradiction, by my definition of turning!) involves "pushing the left tail left to avoid going right." A "good" turn involves "pulling the right tip right to go right." Push vs. Pull. Tip vs. Tail. Right vs. left. "Go" vs. "avoid going." Like I said--complete opposites, in every way!
So--develop the offensive "go" attitude of expert skiers. Then practice, as Rusty described, "left tip left to GO left; right tip right to GO right." Develop the expert's primary defining habit (and perhaps the best-kept secret in skiing):
"Ski a slow enough line as fast as you can, when you can."
We have discussed this concept of the "slow line fast" in numerous prior threads here at EpicSki. Check the archives. If it applies to you, as I suspect it does, it WILL result in an enormous breakthrough for you! Have fun!
PS--Of course, I am making a lot of assumptions here, based on clues from your descriptions, without having seen you ski. I could be wrong!