I think this is just how Motion Plus is for everyone? I got into the habit of re-centering my sword after each swing, which eventually become relatively natural.

It will be interesting to replay the game in Dolphin some day with a more accurate motion controller.

I want Skyward Sword to be released on the Switch for exactly this reason.

Actually, it appears possible to use Switch controllers with Dolphin using this[1]. I may have to set this up in the near future.

[1] https://github.com/yuk27/BetterJoyForDolphin

By going through the thing where you place it on a flat surface?

There's a button you can press that recenters it. Down on DPad maybe? It's been a while since I played.

Yep, you press the down arrow on the d-pad. Fi does tell you about this, but I guess that's the other problem with giving too many instructions—you start ignoring them!