Stunts:
I ride motorcycles, too. Even raced a season in the CMRA before racing made me realize being poor and trying to race just made be broke instead.
While there are similarities to riding motorcycles, I would not go out and ride thinking, "this is how it works on a bike, so this must work on a ski also". I think you will just start getting frustrated trying to understand why one aspect of riding doesn't work, never mind all the other little details.
Counter steering on a ski doesn't work like it does on a bike. There are centrifugal forces acting on the wheels to help keep the bike upright that you need to "counter steer" to get the bike to lean over and turn. When you turn on a ski, moving the handlebar right makes the jet squirt to the right, pushing the hull from the back to spin to the right. If you tried to counter steer left on a right hand turn, the pump will squirt to the left. That means you are leaned over to the right, center of gravity is also shifted to the right (which, if there was no power means you will tip over to the right) and now the pump is squirting left? That propulsion force will want to make the ski power straight ahead but you are leaned over to the right, so voila... you are in the water. Imagine going very slow on your motorcycle, like in a parking lot. Like going around a parking cone at 2 or 3 miles per hour. Your handlebars are turned right, you are leaned right, and you are using throttle to keep the motorcycle going and to overcome the bike's desire to just fall over. If you counter steered in that scenario, can you see how you would crash? Same deal with the jet ski. If you are counter steering on a ski, you are doing a trick.
And just as others have said, face the direction of your turn. I would add to look ahead of your turn as well. Think of your motorcycle again. When you are turning on your bike, are you looking at your front wheel and the ground in front of it, or through the turn? It is amazing to me how looking way ahead of your turn, when leaned over on a bike, knee puck just beginning to scratch pavement, ass hanging off, etc, you are still able to make the turn, but you do. I think it would help you to look ahead of your turn on the ski, too. Start your turn and look anywhere except the nose of the ski. Do you find yourself looking there? Then you target fixate on that spot, that little wave, that little splash, and never get your mind to match where your eyes are telling you to go.
When I started doing turns, my process was: 1) set up my feet, 2) bend my knees a little, 3) look and think ahead of my turn, 4) tweak the steering handlebar a little to get the turn started, 5) feel my balance and shift my weight a little by pressing my foot down into the tray to make the ski "sink" or "bite" into the water better, 5) apply more throttle as the force of propulsion keeping the ski on plane and stable diminishes as that speed gets scrubbed off by the changed angle and friction of the ski's hull interacting with the water in a turn, 6) tweak the steering a little more as I keep working the throttle to keep myself going. Eventually, when you want to finish your turn you will hit the gas even harder and as your speed increases the ski will want to stand up again and you'll be going straight again. When I was practicing turns, I stopped thinking, "I started this turn, and I'm going to finish it!". Instead I said to myself, "I'll start this turn and see how far I can go.". That stopped me from committing to the turn even as I felt the ski starting to go down. Rather, as I felt myself about to go over, I focused on just powering up and getting straight again. Much less frustrating that way, for me at least. Some turns were maybe 10 degrees, some were complete 90 degree turns, and soon they were 180's and 360's. It may be hard to believe me now, but once you get a day of riding in where your turns were just "ok", but at least they were turns (versus crashes), the light will come on and all of this will click. Soon, you'll be putting a buoy in the water to zing around. You'll be seeing how tight you can do turns (like on your couch... handlebar fully cranked over and creating a nice little tsunami in the middle of your circles), and then putting together turns of lefts and rights, combos, etc.
Do you have someone (girlfriend, wife, girlfriend and the wife?) who can video you? Watching yourself afterwards in quiet seclusion in your home, seeing yourself look like a noob really helps you appreciate what is working and what isn't. Make sure you video yourself as close to the camera as possible so you can see yourself as best as possible in all your glorious goofiness.
And remember to smile and laugh at yourself. Riding a stand up is something to be proud of.