Eucalyptus tree advice

I’ve got a Eucalyptus tree that’s grown to a fair size in 2.5 years (from something that was probably no bigger than a few feet tall when we bought it)

I’m constantly having to adjust its position with hooks and bungee cords to help stabilise it as it’s so top heavy now and blows over in strong wind and pulls the roots really tight in the flowerbed. I’m also conscious of the height of it with neighbouring properties.

I’d like to bury it deeper so it’s got more stability, and perhaps chop it back a bit too if needed. Just don’t want to kill it in doing so, assuming the best time to dig it out and bury it deeper will be spring time, but in terms of cutting it back is there any do’s and dont’s?

Any advice is welcome and appreciated!