I fly mode II with no tray specifically (I do use a strap...) but I'm also a 'pinch' flyer... (I hold the sticks like pencils)
I must admit it is a little odd: I've always found the airplane 'WANTS' to turn to the left more than to the right.
I always perceived that as torque / p-factor, but it's the wind direction that dictates which way the landing pattern is flown.
(so, if we're flying a right hand pattern, I fly right hand turns... )
when I was a kid and still learning, I was taught to be very conscious of what my fingers were doing, and to simultaneously observe the airplane's movements.
(I can still hear my Dad in my head... "the airplane is NOT going to go where you want it to go.... it's going to go where YOU command it to go, OR it's going to go where IT wants to go....")
that said, even though torque makes the airplane roll faster to the left, I always found it EASIER to do consecutive axial rolls to the right....
(which is why I typically practice rolling to the LEFT.... I try not to spend too much time on the maneuvers that are easy for me )