Semi-AFK solution ahead.
You don't have to win these
, and as of the time of this writing, it's actually beneficial to de-rank every so often. This will help you put together 5-game winning streaks for better rewards. (edit: this portion is no longer relevant since Omen packs were introduced)
Under Versus, click/tap Battle, and go about your business for the next couple minutes. Once the battle is over, click/tap the bottom right of the screen repeatedly to start the next match. This is a little easier if you have an open reward slot, since you don't have to confirm that "no open reward slots" message.
I popped 1,000 while at work. Please let me know in the comments if this can be improved.