You'll achieve a better aesthetic with this tank if you're able to get smaller plants. If possible, I would recommend replacing the Anubias with Anubias nana or nana petite, and putting some small stem plants along the back (small rotala spp. or pearl weed are options). I think I remember there being a species of val that only gets 6-8" tall that would work as a background also, but I can't remember the name of it.
Java moss generally makes a poor carpet, though it can be done with a lot of trimming. It tends to grow upward and outward and look more like a very leggy bush. Fissidens moss, Xmas moss, or even a split and flattened marimo ball would be better. Another option for either a foreground carpet or midground is crypt parva, though it can get slightly big for a tank that size.
If you do want to try a carpet, you should start from the back and work your way forward, if that makes sense. Like, if you want to just to a small patch of carpet, try putting it between the rock and the driftwood. Or simply cover all of the free space along the bottom of the tank sparsely and wait for it to fill in.
I really like the way your driftwood looks, and with some time and effort, this will turn into a great little nano tank. Good luck!