The first variation is to go from an idle position.
When the right handstick hits the devilstick try to keep it horizontal and toss it about eye height in the air. Then toss the left handstick to the right and catch the devilstick with your left hand. You may have to reach out and snag (or claw) the devilstick with your left hand since it is not in a natural position for your left hand to catch. I try to keep the devilstick as horizontal as possible because it is easier for me to catch in this variation. Then it is only a matter to keep juggling the sticks. To go back into devilsticking you will need to give the devilstick a high, horizontal toss so you can go back into idling.
I have found an easier way to get into the juggle is to give the devilstick a propeller toss to the left side with the right handstick. Then throw the left handstick under and to the right of the devilstick and go into a juggle. You can try to keep the devilstick in a plane horizontal to your body, so that at any time you can easily go back into devilsticking from the juggle.
Another variation is to start from a Reverse Saw position. The devilstick is then spinning in a natural position for the hand to catch it. Also, when you go back to the reverse saw from juggling, the devilstick is spinning in the correct direction.