Re: Juice Press or Greenstar
Two suggestions. First, I would replace the small plastic bowl and the saucer with one plastic container long enough to extend from the legs out to beyond the spout. The bag would sit in it, and any excess juice would drip into it too. When you're done grinding, you could remove the bag, break apart the machine, and scrape the remaining pulp into the plastic container, then dump it into the bag. Much less messy.
But it would work even better if instead of using bags, you simply used cloths. You use the cloth as a liner in the plastic container so it conforms to the container's bottom and sides. All the juice and pulp simply falls onto the cloth. Then you break down the Champion at the end and simply scrape the remaining pulp onto the top of your pile of pulp. All of the pulp is now sitting on the cloth, which you fold, remove, and press.
If you wanted to make, say, 3 pressings, you could begin by layering 3 cloths on the bottom of the plastic container. Then after one pressing, you could continue grinding pulp onto the next cloth beneath it, etc.
Elegant, eh? You could also save time that way by making two cloths full, placing them one on top of the other in the press, then pressing them together.
The only issue I see is the Champion's legs which stick out forward, making it potentially difficult to push the plastic container snugly against the motor body so it would catch all the juice. Either the container would have to be rounded at the end, or it would have to have sloping sides.