hi and welcome to the forum...
cuttlebones are not about beaks being kept groomed they are for calcium..mineral blocks are better and also have calcium....
order two of these perches and place in the cage...the ones saying cement oyster shells...comes in three sizes...id get some soon...place one of them when you get them on a upward angle...see pic. these are GREAT beak groomers..and id say your birds beak is too sensitive now being long to use the cuttlebone...

from what i see the beak is cracking but that second pic isnt too clear to know for sure and yes it does look long...also incorporate some vit. A into your birds diet....with some beet leaf...crushed red pepper seed like you put on pizza ...sweet potatoe....carrot....vit. A is VERY important for many health issues....and give it time offering these because they dont always go for veggies right away it takes many many many times of offering in different ways before most birds will. Under the circumstance id say to make sure the carrot is in small lengths and or diced small and semi cooked to soften it ..and STEAM the sweet potatoe then remove skin to offer.
http://www.birdguys.com/bird-conditioning-perch.html