First, congratulations twice -- once for the new house and twice for having a built-in parking place on your driveway. You will be surprised at how often the trailer gets used as a getaway for folks in your family needing a little peace and quiet.
Second, our driveway is steeper than yours, and we have had no trouble with using ordinary rubber chocks. The heavy duty ones are better. It is very unlikely that anyone will be able to remove them -- the weight of the trailer secures them very well!
Third, if I understand it correctly, the nose of the trailer will be on the downhill side. If that is right, you will have to extend the jack pretty far, which is going to be pretty wiggly.
So to prevent that, stack a couple of very hefty wood blocks for the jack to rest on. The jack stem will be shorter, and the trailer will wiggle a lot less. And if you need to, do the same thing for the front stabilizer jacks.