The pointy growth is a new pbulb and probably has no roots yet. It can be repotted now. Don't water it for a couple days before repotting it. The roots get more limber and there is less chance of cracking any of them. First take off all the old sheaths from the pbulbs. I usually grab them between my fingers and split them down the middle so I am just pulling off half a sheath at a time. This makes it easier. I then lay the pot on it's side and grasping the oldest pbulb by the leaves I gently ease the cym out of the pot. All of the new growth buds are on the outside pbulbs so be careful not to grab before looking where you are grabbing. I take a phillips screw driver and start teasing away the media that comes off easily. Kind of roll the root ball around. Also start at the bottom of the root ball and work your way in and up. There probably aren't any roots of any consequence on the inner/upper portion of the root ball under the older pbulbs. Take your time slowly easing out as much of the old media as you can get out. If you break a few roots, no big deal. Just work out the old media. It should be fairly easy since this looks like it was repotted two years ago. What was it potted in? Spag? I like bark. Some sponge rock for moisture retention and some charcoal as an anti fungal/bactericide. Once you have the roots clean or nearly so, I take a hose and wash as much of the old remaining material off. Once you have it cleaned you can look around the bases of the pbulbs looking for very immature growth buds. Next you can repot it. I hold the cym up by the leaves with the roots dangling down into the pot and slowly pour the media into the pot around the roots. Pour in a little, tap the side of the pot. Pour in some more and tap the side of the pot. This way the roots are hanging down into the pot while media is settling around them. When you are halfway through filling the pot with media I firmly set the pot on the work bench a couple times to help settle the media and then continue until the pot is full. The base of the new growth should be at least an inch below the top of the media. This will encourage the new growth to push it's roots down into the media. Hope this helps.
For some reason, there are no longer any photos on this thread. What happened?
One of several things you did not mention was not to let the roots touch the bottom of the new pot. This will cause a quick rot. Just before you place the division in the new pot, you would be wise to cut the roots to no more than 3" from the base of the pseudo bulb. This also encourages them to branch. Long, broken roots will just die.
I also would NOT recommend large bark as it is way too easy for most hobby growers to grow "too dry", something Cyms definitely do not like.
My Lady, would you please explain your premise about not letting the roots touch the bottom of the pot (which is absolutely correct) for the new growers here. Information like this is so important it should come with the explanation...why. Info like this is what turns new growers into seasoned growers.