Re: Hi-Hat Stepping (Lift & Close on every beat)
This is a great thing to work toward. The left foot is so overlooked, mainly only viewed as a way to play double bass. The left foot is the drumset of the drumset - it does for the drumset what the drumset does for the entire band: Timekeeping and anchoring. But you can do so much more with it.
Pump your heel up and down while you play with the hats closed or keep it moving up and down while you play ride, getting a neat ssssip out of it to accent something or mimic the melody.
I was fortunate in that my first teachers taught me to always keep the left foot going on the hats. either with whole, half, quarter or eighth notes. I can now play clave beats on the left foot (hooked up to a pedal-activated wood block) and play the hats in three while everything else is in for, or keep the hats going with quarter notes while playing in 7, 9, 11 or other unusual meters.
The advice here is good. I would suggest integrating it from the beginning. Go back and get it going in whole, half, eighth and quarter notes in a simple rock rhythm, the move to the next most-simple thing you have, then the next, and so on. With a short time, you should be integrating it into whatever you are doing now. The integration will go more slowly the closer you get to your current level.