I did something similar in my game with a puzzle that required at least one of the characters to voluntarily go unconscious. The character’s spirit had to accomplish a task while the other characters protected the body. It worked pretty well.What about this thought. (I'm assuming that the PC's will have at least 1 guard on watch.. otherwise, I could have perception rolls to have someone(s) wake up).
2 Hazards. hazard 1 is the "awake" hazard. it is the PC or PC's who are awake working frantically to prevent their companions from getting dragged into and merged with the tree spirit, and avoiding the same fate as other branches are moving around trying to grab the players that are awake.
hazard 2 is the "dream" hazard, for those that are already caught. here, they are fighting the drain of their lore. successfully fighting this will slow the tree's ability to merge in hazard 1. and failing to try and slow hazard 1 will make the knowledge extraction harder in hazard 2?
To get back to your tree spirit issue, what is the tree spirit’s normal operation when it isn’t attacking the characters? If the spirit was tricked into attacking the characters, maybe something like Diplomacy or Deception skills using the influence subsystem would work. If it was corrupted, maybe something like Nature (even if it isn’t corrupted, Nature should be a useful skill to use). You can throw in some Acrobatics checks to avoid branches.
Finally, what if you cannot talk to its “limbs”? To effectively interact with it, you need to reach its “face” which requires Athletics and Acrobatics checks.
Also, check out the Research subsystem example in the GMG. It can be made similar to what you are describing with only a few tweaks.