Asymmetrical boards are made so your backside has a quad setup and frontside has a twin keel setup. Concept is that backside pumping is best with looseness of quad and you get the frontside stiffness of a keel.
Maybe if you pick up a quad or twinzer, you may have more control. I know what you mean with this post. I agree that foot placement has a lot to do with it. I learned to crank turns on my classic fish when I had my feet back on the board rather than up the nose which creates a weird pivot point.
Oh sweet baby Yankee sleeping in the manger, not an asym..... I personally take offense to these boards. Mainly because I'm jealous of people that surf such perfect waves that they have to tweak their equipment so much that one side can't be like the other. Gat Dang Ridiculous. It reminds me of hyper-adapted species of birds, reptiles, amphibians on isolated islands that would never make it in other environments.
It's been awhile since I rode a twin, but I remember that on larger waves you need to go down and out in the flats and draw the turn out so you don't spin out. Get low, in a crouch so you are centered over the board. On smaller waves, which is what they are best in, I personally like the skatey slidey feeling. Throw some tail, go vert, surf it rail to rail, bust some 360s, cause they don't like to go straight down the line like a thruster ( hence the name ).
Drop in straight, get your speed and level the board. Once you are centered then lean back a bit and crouch a bit....this will be your bottom turn. Once you're turned and heading back toward the wave...carve up to the power source and drop down the line. You'll have too much speed...enjoy
I feel that you can drop in with less angle and work on your bottom turn to stay out in front. Also, there's a tendency with most surfers to to place their feet too far on the inside rail. Make sure your pop up is dialed and consistent. Just saw this new product that promotes better foot placement. www.bit.ly/surfsols