For me this isn't terribly difficult. Play the lower staff with the left hand, the upper staff with the right. I use 2 and 4 in each hand since they are more even in length. However, I might change that to take the F# in the left hand with 3.
Play right hand over left, not left over right. It's harder to hit the G# in the right hand when reaching under than it is to hit the F# in the left reaching under. (Try it for yourself.) Play the right hand white keys up towards the fallboard, putting your fingers between black keys. Play the left hand out towards the edge of the keyboard, reaching in slightly to take the F#.
See how that works for you. :)