There is no solver like that in Final IK, sorry. CCD and FABRIK can't solve for both the position and rotation of the target, just the nature of those algorithms. Algorithms that can do that, like inverse jacobian, are way too slow for game development, which is why I have not made the effort to add them in. It is possible to set it up with Unity phsysics though, if there is no animation playing on the tentacle. Here's an example package for you.
Basically just set up the tentacle with rigidbodies and joints, make the first rigidbody kinematic and add a target that matches the position and rotation of the last part. Make that target a kinematic rigidbody too and add a FixedJoint to link it to the last part. Then just add the InverseDyncamics script to the root. It will make the rig behave like an inverse dynamics solver pretty much.