As you see, I decided to put a piece of metal (which came with the shop press) on top of the piece of wood so that the rod wouldn't break the wood easily.
I have two issues. Some amount of juice leaks out of my Champion during grinding so that I would have to put something under the motor shaft to collect it. What's more annoying is that the juicer tends to keep more pulp inside when I finish feeding vege/fruits than it would with a screen on the bottom. So basically I would have to break it apart (which is not complicated but it can get real messy) and grab the wet pulp and put it in the bag before I press it.
Other than that, I'm satisfied with the juice quality (supposedly with maximum nutrients, right?) and its taste.