I have been growing this plant for a bit, Its an appressed climber, which means it grows very close and flat to the surface it grows on. It will latch onto just about anything, and 'shingle' up the surface.
In your photo, you have it upside down. Leaves of Rhaphidophora generally point up and out, leaves of immature shingling Monsteras like dubia generally point downward.
It also looks like you have some nice roots. And it looks fairly mature, judging from the size of your glove next to it.
All you would need to do it to plant those roots in the soil at the base of your palm tree, press the plant against the surface of the palm and keep it moist and humid. It will latch on and start to climb.
My second question is about the palm. Is it a palm that you have to trim, or is it a self-cleaning palm? Once the shingler starts to really cover the trunk, will it be in danger of being dislodged by the fronds coming off or being trimmed off?
Rhaph. crypt is not a 'morphing' Rhaph. The leaves will enlarge and get to a very large diameter in very mature plants (I have seen dessert plate sized leaves) but it does not change form into a different type of leaf like some of the other Rhaphs and Monsteras do.
This is one of mine. I have it growing in 2 terrariums and out in my greenhouse on 2 supports, one a 12 ft tall coir sparred totem and the other an 8 ft tall coir covered fencepost