Shameless plug-in *cough*
I was a bit sloppy in the demonstration, but using bunnymen for Crab King is really effective and quick. 15 bunnymen were used to kill him in 2:15. It's a set up that also allows you to redo the fight multiple time. That's how i'm getting my ornaments this year actually, it's way less stressful of a fight like this, at least for me.
Though for all the parametres you have to take into account, doing the fight normaly is indeed really hard when you consider that the celestial altar is mendatory if you wanna advance the plot of the game. Luckily, like others have pointed out, it's a fight you really only need to do once with the pearl and call it a day. Get through the trouble of killing him just one time and you'll be set (unless you are a ornament maniac, then good luck on your irl sanity).