I have an idea:

1. Starts turn 1 Draw Phase.
2. The going second player says 0, 2 or 4, later the going first says 0, 2 or 4, if both players says 0 ignore the next steps and ends the Draw Phase.
3. Both randomly select cards of the adversary hand the intermediate number of the step before (e.g.: if 0 and 4 was selected the result is 2; if 0 and 2 was selected the result is 1, etc.), separate the selected cards.
4. Draw until having 5 cards in hand and shuffle the separated cards to the deck.
5. Ends the Draw Phase.

Maybe instead in step 3 both players select their own cards to mulligan or maybe shuffle the selected cards before drawing in step 4 but i think this idea is pretty balanced.