What should I look for in an astronomy tripod?
I have the exact same binocular, and in fact I also have a very similar tripod and head. I'll take a photograph this evening to demonstrate my setup.

I am very happy with the setup, and I find it very stable. I usually sit the tripod on grass, but I do not recall ever having a problem with it on concrete or stone. I do try to keep the neck as short as possible, and use the legs for height. Also, the binocular can have it's tripod mount moved fore or aft, I think that mine is in the full aft position.

You might be able to hang a large mass (bag, perhaps) from the underside of the tripod; you should find a hook already there made specifically for this purpose.