Looking good! I assume you are using it in conjunction with a bottle-jack. I have seen excellent results with such a setup. If the pressure from the jack is primarily pushing between the cross-support and the top support, and there is no gap between the tray and cross-support, then the tray should hold up just fine.
If you haven't done so already, you will definitely want to give it all a good coat of food-grade wax (Beeswax, Carnuba, or Shellac are all good food-grade options). That will help protect the wood from degrading and softening over time with exposure to the acidic juice.
Also, you shouldn't be using any type of chemically treated wood (wax only) on any part of the press that will come into contact with your juice. Based on the picture, it looks like only the frame is treated wood, which is fine. If any parts of the tray are treated lumber you will want to swap them out with untreated wood.
The garbage disposal grinder is a good idea. I previously used one that I built with great results. The only hiccup with a GD grinder is if you are grinding large amounts of fruit then it needs periodic rest breaks to keep from overheating.