What can I do to prolong vegetable and meat freshness in the freezer?
For most vegetables, it is very difficult, if not impossible, to retain their quality once they have been cut. Your efforts would be much better spent either improving your cutting/chopping proficiency or in cooking entire meals ahead of time. Also, you could prepare components, such as sauteed onions or peppers, and maintain relatively high-quality versions of those.

Meat is a different story. You can do preparations in advance, and freeze individual portions for later use without degrading quality.

The best way to avoid freezer burn is to have a very cold freezer (ironically, easing the cooling settings on your freezer was having the opposite of your desired effect), and to prevent your food from coming in contact with air. You can use a freezer bag for each food item, making sure you squeeze all the air out of it first. However, if you are really serious about this, you would be well-served by investing in a vacuum sealer. Air is the big enemy here, so mechanically removing air from the system will greatly extend freezer life.