Well you just said no bamboo but I have multiple 7' x 2' stock tanks planted with (originally) one #15 Phyllostachys aurea (golden bamboo). They are huge, lush and I've had no trouble with them. I use drip irrigation which admittedly I leave on for about 45 minutes. We use them as plantings around our metal barns, which really needed softening, but are surrounded with concrete and gravel so I had to do tubs. I think the key to growing them in pots is to use a big enough pot. I also suspect that after another 3-4 years (they've been in for 3) I will have to have them pulled out, cut up and replanted.

All of that may be WAY more than you want to do, I just wanted to let you know that it is possible to do and would make the right kind of screen.

I had the same issue. I finally put up a little wooden slatted roof from the house to the fence and I grow a kentia palm in a pot under it. I have some nandinas on that side of the house too, but I don't know how they would do in pots.