The stickier tires could actually cause more problems. If they slip and then grip again at the wrong time, you could be going from a minor lowside to a highside, and there's no such thing as a minor highside.
Chicken strips have very little to do with anything other than body position. My track tires have none, but my street tires have an inch or so of chicken strips.
And no, I would not recommend you trying to "gum up" your tires by pushing too hard. Even with your current amount of experience, there is no need to push tires that hard on the street. That will cause you to crash, no matter what kind of tires you have.