Yes, I like your ideas. I was unsure about wanting triffids to be able to move. They can in the movie, so I thought it was acceptable here, but having them be largely immoble except for special ones seems better. Your idea also means they also would have diplomatic clout instead of being something like gray goo that all the races oppose. I think there needs to be some way for triffids and the animal races to communicate. Maybe triffids could hijack someone's mind like with Brent Spiner in Independence Day. Perhaps they could present themselves as the poor victims of vicious deforestation genocide by the other races, encouraging them to enact policies of plants rights, while actually the triffids are planning the downfall of civilization. Another way is to make them mostly but not entirely alien, so the other races aren't really sure whether they are intelligent and thus some of them act carelessly around triffids, thinking they are just mindless plants.
Furthermore, the idea of triffids trying to convert the world into one giant triffid grove sounds great to me, as it means they are not stereotypical nature-defending druidic things. They don't want to maintain the natural order or prevent the environment from being changed. Rather, they just want to ensure that it is changed to their liking, meaning they're ultimately not different from the other races.