I use buckets with holes drilled in the bottom to contain mints, bee balm, lysimachia, etc. when I plant them in the ground. With mint at least, you have to leave a couple of inches of the bucket rim above soil level (soil level both inside and outside the pot) or they will flop over and root that way. I was lucky to find some black buckets that absolutely do not show at all. You could spray paint a white bucket black - or you could find some huge plastic pots that maybe someone got some bushes/trees in. I bought some of those from a guy at a flea market.....
There ARE ways....
Also, I think that when I redo my friend's bed I might just leave those Houttuynia in there, remove the crummy looking plants, and underplant the Houttuynia with tall things..... BULBS, certainly, but maybe rudbeckia, etc.