Sounds like you will need a different juicer altogether.
Like the 'Wheateena/Marvel (Red Label)' or the 'Professional MJ475'. I regret that I would not endorse the Miracle (even their new stainless model). Additionally, grass juicers DO NOT do a veggie juice.
Most people in the long-haul end up with TWO different juicers.
Although many masticators MAY do a 'grass' or 'sprout' juice, you will be much happier with a dedicated model. The precision for the nozzle requires closer tolerance than a normal 'veggie juicer'. Unless you are willing to personally test all the new masticators that advertise as a 'veggie/wheatgrass' juicer. I would love to hear the results of the effort.
On the other hand, occasional grass juicing
is OK with a 'Twin Screw'. My antique Champion does a FAIR grass, BUT that is another story.
The 'Green Power' is quite different from the other 'Twin Screw' juicers.