Sorry it took me so long to get back to this. I would do two things: prune manually to get it down to a reasonable level and then add an herbivore. From how large the stems are in the picture, I would recommend that when you prune it, you don't just go in and rip it. Find a stem that will break off a decent chunk and pinch it hard for 30sec or so and then tear off (to try to get the macro to close its vascular system off before you break it).
Mithrax crabs are a good place to start herbivore-wise on stuff with thick stems like this, but you'd probably only want one (they can be territorial), hence why I recommend going at it by hand at first. Just make sure you don't force a Mithrax into exclusively eating the stuff or they will exhibit their more omnivorous tendencies on tankmates. They need some meat every now and then to be healthy. Urchins are also great grazers, but the common species in the trade that are good for that also carry stuff - so that's something to keep in mind if you have any little things that you want to remain in place. Also, Mespillia globulus (tuxedo), which stay smallest, may not eat this species. I'm pretty sure Tripneustes gratilla (sometimes also called tuxedo, but also other common names) would chow down on it, but they get quite a lot bigger than M. globulus.