It's been a while since I did this. That looks like the right part, but if I remember correctly I went to the dealer and got it, it wasn't crazy expensive.
I would go to fordparts.com and check to see if it's correct.
Also, from your description, you may be lucky and it's just the actuator, if you take the old actuator off and the lever moves freely, it's an easy fix. If it's hanging or partially stuck, you have a partial jam.
From reading the forums, there are other ways to get to the jammed felt from other members. The official way is what I did. Other's have found a way to access behind the radio by either cutting or I read someone who found some kind of access way without cutting? I would do that now knowing what I know.
The only good think about pulling the dash is you get to really know the interior of the truck, and when you put it all back together with lock tight it's SOLID.