Continuous smooth camera movement in post
As Duvrai mentioned, the docs for Final Cut's InertiaCam setting do say it will handle what you're talking about, but I've never tried it myself. 

If you are familiar with the 3D aspects of AE as well as simple AE motion tracking, you could try the following technique. It's a little involved so it's usefulness depends on how important the shots are to you.

First turn the footage into a 3D layer and then apply an Animation->Track Motion to that layer. Change the Track Type to Stabilize. (This is how to access the older, simpler AE stabilizer, as opposed to Warp.)

Stabilize the footage using a position track point on a good spot in your panning shot. Pick a spot with lots of screen time during the pan. Apply the stabilization. Afterwards, if you switch to an alternate POV like Custom View 1 and scrub through your footage, you should see your footage slide left/right in 3D space synced with what your real-world camera did.

Next add a 3D camera layer and keyframe it's position to make it 'shadow' what your original camera did, but this time using eased keyframes instead of a tripod. This effectively creates a more ideal motion laid on top of your original real-world movement.

Obviously sometimes the original footage will go out of the 3D camera's view when the original doesn't match the ideal. To remedy, cleverly add a few more camera position keyframe to throttle the AE camera's velocity over time, or simply use scaling keyframes on the footage layer to smoothly 'zoom-in' occasionally.

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