Hi Craig,
Let’s see; first of all, welcome to the world of Subdivision Surface Modeling.
These ‘pointy bits’ are causing most of the problems:

Also, this Face is quite distorted (I Duplicated it for visuals):

The easiest ‘solution’ I can think of at this moment (almost midnight here, so I might not be very fit anymore😉) is something like this:

(The more ‘Quaded’ the Topology is, the better the result.)