I'm not sure if the pro drummers would say this is a god idea but you might play open handed for a while.
I started out playing open handed and my teacher made me change to cross hand.
Even though I have only been playing a few years, I have become quite adapt at changing my rhythm hand from left to right. In fact, it's not unusual for me to switch in the middle of a song. Especially a long jam.
I start out playing the snare with my right and the hi-hat with my left (which is typical for me) but when I play my ride cymbal (which is on my right) I often switch to playing my snare with my left hand and the ride cymbal with my right. Even for a novice player I seldom miss a beat in between.
My teacher really freaked over this at first but eventually realized it was really making me a much more versatile drummer.
Like I said, most pros probably wouldn't recommend you do this but it seems to be working out for me.