shadowplay not recording entire taskbar

Not sure why you're expecting it to show the Windows taskbar (if that's what you mean) while in game. Only way it would do that is if you are either playing in windowed mode (non borderless) or at the desktop instead of in game. Either way, to record the desktop you need to go to the "Privacy control" tab in ShadowPlay and set "Capture desktop" to On.
 
Ah, I see it now. What res is your display? Reason I ask is it might be an oddball size ShadowPlay can't fit exactly (1366x768, etc). I take it you see your full taskbar while not recording? Otherwise it would be a simple resize issue, which can be handled in NCP.
 

In ShadowPlay do you have Video capture res set to 1080p, or In-game? The default is In-game. I always set mine to 1080p and have never had the problem you're describing. Then again, most people don't capture games as a small window set into their desktop, including myself.

It could just be that ShadowPlay is a bit quirky with that scenario. It might also matter whether you're playing the game in Fullscreen or Borderless mode, and whether the game res is same as your desktop res.