2-beat kick & domint leg.
When I now try using a 2 beat kick in spear switch, my transition from right arm skating, across to left, feels pretty good (with a right leg kick). But switching the other way, I am completely unco-ordinated, and more often than not I end up kicking again with my right leg, and balance goes out the window.
The above description is usually the result of the dominant leg always kicking first. (It is usually the right leg that is dominant and that fits your situation.) When you kick with the wrong leg first - you then need the second kick to rotate. So you are not uncoordinated, you just need to sort the kick out.
I am not clear on what you have described for your drill. Just be clear on knowing that as you spear, it is always the opposite leg kicking forward.