We just model a rigid to represent the wing valve and apply displacements there. Make sure that all the displacements are filled in with the 'unused' degrees of freedom in any case set to 0. Essentially we are assuming that the tree does not deflect or rotate as it moves. Simplified to the bone, but getting relative stiffnesses of things like xmas trees is never going to be easy.
For what it is worth, let me know if you want any other input. I've done a fair bit on this recently and am happy to help if I can.